First of all, it is important to notice that the answer to several of your questions depends on whether you intend to play on Single Player or Multiplayer. The strategies, requirements, templates, etc. are different. Given what you say I'm going to assume you ask for Single Player, so keep that in mind.
a) Is it best to recruit/train armies in groups of 24 so as to create an entire army at one time? What about special forces? Is it the same and how many special forces do you need?
You don't have to train in batches of 24. You can train less and then keep adding, or train larger numbers and split them later. Special forces have a cap: you have a base amount of special forces batallions you can deploy or a % of the total batallions you have deployed that are not special forces, whichever number is higher.
Special forces are useful, but usually in SP you can usually get away with not using them and doing different strats, but of all 3 the most useful are marines (amtracs and amphibious tanks also count as special forces and are used for the same purposes as Marines, which is naval invasions and combat through rivers). Paratroopers can sometimes be useful but are quite niche, and mountaineers IMO are pretty much useless.
b) 20 or 40 combat width?
It depends. Usually when you are on the offensive you will do better with 40 width, but they require more manpower and equipment. As USA you shouldn't have either of these problems, but it could be quite an issue if you are playing a minor and fight a war in 37. A good template is usually a 14/4 (14 infantry, 4 artillery). Sometimes if you plan to fight in low supply areas you might want to use something smaller like a 7/2. Is not as good as a 14/4, but requires less supply, which in some cases can come in handy.
Tanks, and especially, 40 width tanks, are 1v1 the best offensive tool, but they have their downsides: a lot more supply requirements, intensive fuel needs, and hefty penalties if used in naval invasions, through mountains or marshes or in adverse weather conditions, on top of a lot of production needed. As USA this shouldn't be a problem, but keep it in mind because in SP you can get away with not using tanks if you don't want to consider all the factors.
For defense, 20 width is usually your best option (10 infantry batallions). However, if you just want to garrison the coast against naval invasions, you can get away using 10 widths (5 infantry) with engineers, the AI will more often than not lose against those if they are entrenched, and you will save a lot of equipment and manpower (this, however, would be suicidal in MP).
c) During the game, the allies were forcing the Germans out of France. I committed three whole (24 unit) armies to the fight but soon found that the Germans had rebounded and were forcing the allies off the continent. It was all I could do to get my troops out of there. What happened? I did not get any indications that the Germans all of a sudden found extra men and equipment and threw it at me.
Could be for many reasons (hard to say without seeing what happened exactly), but the first that comes to mind is supply. Your AI allies will flood the frontline with troops (much more than the supply limit allows) and this will affect severely the combat capabilities of your divisions and cause attrition. This is a known issue with the game and the main reason why I recommend to never call any AI allies to your wars unless is your last option. Believe me, you have better chances in Europe as USA if you declare on the Axis yourself and never join the Allies, nor give them military access.
In addition, the AI is coded to prioritize combat against a human opponent. They will gladly let the Soviets get to Berlin as long as they stop you if they have to choose.
d) Where are my generals? When I create new generals, I kept getting ones I have never heard of. Where were the Galvins, Devers, Smiths or Ridgeways?
Most countries have a certain amount of designed generals and that's it. If you hire new ones, they will be generic generals with random names and traits.
e) Is planning really worth it? Do I really need to go into all the trouble of laying out a front, determining an axis of advance that then executing?
It is worth it. Planning adds positive modifiers to combat. For instance, say you have 30% planning bonus: when you attack, you will have a 30% bonus to your stats in combat. If you use it with the battleplan (clicking the go arrow) it will decay slowly, and if you micro, it decays 3 times faster. However, there are downsides, as clicking go on a battleplan is not a good idea unless you have a massive superiority over your enemy. Micro will be better as you can make encirclements, and push where you have the advantage without engaging in unfavourable combats (losing additional men and equipment).
f) What is the best way to use your allies? How can you better coordinate strategy and objectives?
The best use of your allies is not calling them into the war. Seriously. You cannot coordinate with them at all (assuming they are AI).
Sea/Naval
a) Is it better to have a number of fleets (10 max) under a single commander or spread them out? With this type of set up, I had only three different leaders (Nimitz, King, and Burke). Should I have spread them out in order to use Halsey, Spruance, Mitscher, etc.?
It depends on what you are trying to do. If you are convoy raiding with submarines, or escorting your own convoys with destroyers, it is better to have them divided in several task forces (in order to cover more sea zones more efficiently). If you are trying to naval invade or to fight a big enemy fleet, it is better to stack your ships (with certain considerations, such as not using more than 4 carriers per task force, and ensuring you are properly screening your capital ships, among others).
There is no need to divide your forces with the only purpose of using all your admirals. I recommend you use different admirals when you have fleets doing different missions: for instance, one admiral will take care of all your sub taskforces (each admiral can have up to 10 taskforces), another for naval invasion, another for convoy escort, and so on, since they will be (probably) operating in different areas.
b) Where were my naval experience points? I kept getting into convoy battles and an occasional fleet engagement but never seemed to increase my points. Why?
I've never cared about looking at the exact numbers for this, and probably somebody else can give you more detailed information in this regard, but I've noticed that, in general, naval experience is generated much more slowly in combat. Best and fastest way to gain navy xp is to train your ships. Be careful with fuel initially, USA starts with certain modifiers that dramatically reduce fuel gain from oil and you won't be able to sustain training indefinitely your whole fleet. Make sure you also assign dockyards for repairs, as the ships will get damaged during training.
c) Why did it seem to take so long to conduct an invasion? Seemed like every time I planned there was some region that didn't have enough intelligence despite me having units already there.
I'm not sure I fully understand this question: why would you naval invade a place you already have units in?
In general, intelligence is not based on having a unit somewhere, but rather on actual intel on the target country. Normally, when your naval intel on a country is below 40%, you will get penalties to naval supremacy, which is what ultimately determines if your invasion can go or not. Important to notice you want to have intel on the country whose fleet is preventing you from launching, not on the nation you are landing on (which may or may not be the same).
There are several things you can do to get intel on your enemies: the most obvious and common one is assigning spies (getting intel networks, infiltrating missions, etc), but also engaging in combat: the more you fight on land against your enemy, the more army intel you'll get, same goes for navy. In addition you could also use recon airplanes and radar, but this is usually marginal and not worth the cost to pursue (with rare exceptions).
Air/Air Forces
a) Tactical or ground support or strategic bombing? I have always been a fan of strategic bombing, but is it worth it? Playing the USA, you are never on the receiving end of a strategic bombing campaign so it is hard to determine what the effect is.
All 3 have their uses. If you manage to get air superiority, having mass CAS can be the difference between getting stuck or steamrolling your enemy, it is quite powerful.
Strategic bombing can also be really useful, if you manage to mass strat bombers, and your enemy is unable to shoot them down effectively, there's a lot you can do with them: destroy their factories (reducing their ability to produce more equipment), bomb airports (rendering their airforce useless in certain areas), bomb their ports and infrastructure (to affect their supply, although this has less impact against AI than against a human player), and so on.
Tactical bombers have 2 advantages: versatility (can do both of the aforementioned missions) and range (quite useful in areas with big airzones, such as China and the Pacific). The downside is that they don't do either of the missions as effectively as CAS (unless they got no range) and strat bombers.
Don't forget about naval bombers, they are a nightmare against ships. Tactical bombers can also do naval bombing. Less effectively in equal conditions, but again, have a lot more range.
b) Where do you put the airplanes? Seems like there were never enough airfields overseas. Since you don't want to pay a penalty for having too many aircraft at a base, what is one supposed to do?
You have to build airfields. Each level of airfield provides room for 200 planes (of any type), with the maximum being level 10. Deploying 1 more plane than the airfield allows is as good as having 0. This is another of the reasons why I don't recommend to call an allied AI to your war. They have a particular fetish for overcrowding airports you are operating from, without you noticing, and making your airforce useless.
Homefront
a) Is spying worth it? Can't find any videos that really explain it. If it is worth it, does it make sense to become the faction's spy master to get more spies?
Very. There's plenty of things you can use spies for. The basic is to use them to establish an intel network on an enemy country. The higher the % (max 100%), the more intel you get on them on all 4 branches (civilian, army, navy and air) and the more missions you get access to. Missions to infiltrate a branch will give you bonus intel on that branch even if you lose your intel network, and open the possibility to steal blueprints. You can also capture enemy ciphers (to speed up the decoding process), boost your ideology, stage coups (starting a civil war in the target country), and several other things.
Additionally, spies can reduce resistance in occupied areas, and reduce the enemy's frontline combat capabilities (if your intel network reaches the enemy frontline troops, they will have reduced planning bonus and entrenchment, based on the strenght of the intel network).
How to use them is situational. It depends on what country you are playing and what you are trying to achieve, but more often than not you will have good uses for them.
b) Should you max out on building slots? In other words, if a region has 20 slots for construction, should you build 20 factories, etc. or should you save a slot "just in case"? In addition, should you max out on docks in a given region?
Eventually, yes, although it is quite rare to fill up all the building slots in your nation unless you go to the late game and have a massive industry, more commonly your game is done before that (USA might be the best candidate to fill up the slots though). As a rule of thumb, you want to fill first the regions with higher infrastructure (it allows to build faster), but there are exceptions to this.
You don't have to max out docks in a particular region. As long as it is a core region, a dock in an area with no infrastructure or not connected to your capital via land (i.e. Puerto Rico if you core it) is the same as a dock in New York. Same goes for other factories.
Just a recommendation: factories are very important, yes. You should prioritize them, yes, but don't forget about your infrastructure and naval bases. As USA, you will 99% of the time be fighting overseas. That means supply will go through your ports. The higher the infrastructure and the level of naval base your supply goes through, the better (although supply is quite a topic on itself, and is the main focus of the next rework, there's quite a few threads discussing this in detail if you're interested).
c) When you select a company/firm etc. do the benefits remain throughout the game or only when that particular firm is selected or do you lose those benefits once another entity is selected? How about for the theorists, political appointments and military staff?
Companies provide the displayed bonuses, but only to equipment researched after you get the company. For instance, let's say you research Fighter 1 without the company: it will never receive the bonuses for it. But, if you get the company, even 1 day before the research for it finishes, then the bonuses will apply for that equipment for the whole game.
Theorists will give you a trickle of xp daily (army, navy or air, depending on which you choose) from the moment you hire them. Likewise, the bonuses they provide for doctrine research apply from the moment you hire them. For instance, if a doctrine research takes 100 days, and you hire a theorist that gives you a 10% bonus for it, it will take 90 days, but if you hire him when you have 10 days left, it will take 9. It is not exactly like this, but just so you get the idea.
Political advisors and military high command will apply the bonuses to all relevant instances as soon as they are hired. If you remove them, or substitute them for another, the bonuses no longer apply.
Many thanks for any responses!
My pleasure!