I am not sure I can fulfill all your desires because I really don't understand how "combat" works in HOI4 and the effects of infantry, armor, artillery on each other or the effect of the "attached" units of other types. (communications, medical, recon, AT, AA, engineers, recon etc). But I think I can give a little "primer" on WWII division structure.
Divisions became the basic operational formation in WWII for land warfare for pretty much all nations that had significant military. What that means is that when you wanted to move troops to do something (attack, defend or regroup/rebuild) the division was the basic unit that got moved. (There are numerous exceptions to this in that in areas where troop density was very low (lots of space and few troops) (the Scandanavian countries including Finland and North Africa or even the Soviet Union at times of exploitation or attempts at recovery from defeat) or when divisions needed to be "reinforced" for specific attacks (say extra engineers or artillery to breach a fortified position or cross a river {these extra troops usually came from Corps or Army reserves}.
WWII divisions usually contained
1) a headquarters unit (commander staff etc)
2) 2 to 3 regiments or brigades as the primary maneuver force of the division (note as I am using these terms a regiment or brigade consisted of 2 to 3 battalions of men where a battalion is made up of 500 to 1,000 men based on type and army policy (and regiment or brigade is then up to 2 or 3,000 men when full strength). The US and Germany in WWII used "regiments" as their terminology while the British use "brigades". In any case the primary maneuver units were either infantry (including mountain, jager, cavalry {ok I am cheating here}), armored or mechanized infantry or armored {panzer}. These are the "front line" fighters that are in contact with the enemy when the unit is in combat. While the name may be "infantry" or armor that does not mean that everyone in these units carried a rifle or machine gun or drove a tank. Most battalions and regiments had heavy weapons components or companies that had heavy machine guns, mortars, sometimes even light or medium (up to 75 mm) guns or howitzers, some anti tank rifles or things like bazookas/panzerschreck etc.
3) An artillery regiment/brigade -- Pretty much all nations knew the value of artillery and if they had the resources put 3 or 4 battalions of artillery (2 to 3000 men total and maybe up to 100 guns/howitzers 75 mm to 155 mm in size in their divisions if they could.
4) direct combat support units that showed up on the front lines -- These are things like --
a) engineers that are very helpful at building and fixing things like roads, bridges and buildings that men in the field need to operate most effectively, They also may be useful in assaulting fixed/hardened positions etc Engineers at the division level usually came as either battalions (500 to 1000) or companies (100 to 200) and in war most of the time more is better.
b) reconnaissance Units -- These are what used to be termed scouts, light infantry, or the role of cavalry -- they possibly move faster than a "normal" unit because they are smaller or more lightly equipped or have a few extra light vehicles -- Their job is to make sure the division knows what it is getting into if it moves and to have "early warning" if something is coming its way. Many nations put a recon battalion in their infantry divisions and particularly in their more mobile divisions (Armor/Panzer or motorized) to send out "exploring" when there was a breakthrough.
c) Anti tank -- Specially equipped units to kill tanks (with obviously anti tank guns and later mechanized s/p antitank guns) Quite commonly these were in battalion strength in many WWII divisions.
d) Anti aircraft -- Specially equipped units to kill airplanes (obviously anti aircraft guns) -- these usually came in battalion strength units and were less common in divisions than the AT units. On the other hand, with the success of the German 88 mm AA gun at killing tanks as well as airplanes the Germans at least kept trying to add more.
5) General support units that no one wanted on the front lines but sometimes mistakes happen
a) Supply -- these are the guys that move food, water, fuel, bullets and anything else an army needs from corps supply dumps to the guys actually doing the fighting. It actually takes a lot of effort from a lot of people to get the right thing to the right person at the right time continuously. (logistics is really important in war)
b) Communications -- keeping 10-15,000 men on the same page and doing even the obvious things to support one another is really difficult in the "fog of war". Ideally these guys make sure that two different regiments hit the same position at the same time from different directions and that the artillery is well coordinated and hits the enemy and not are own troops (minimize "friendly fire" casualties).
c) medical -- control disease, sanitation etc so you don't lose more people to disease than the enemy (up unitl about WWI disease did more damage to armies than the enemy) and take care of wounded so that the likely wounded can get back into action and everyone who fights feels that if he is hurt he will be taken care of and has a chance of surviving.
d) Military police -- maintain order (an army has a lot of guys with guns running around and if they get out of hand can do a lot of damage to your guys rather than the enemy) and also act of traffic cops (so Patton doesn't have to do it -- film reference) as well a protection against and local population objections to the presence of the division. (Most civilians would rather not have an army division camping out in the neighborhood much less a hated invader).
e) whatever I forgot e.g. US Marine divisions have an air wing (50 - 100 airplanes) assigned for direct air support
What I can not do is figure out how all of these things come together in HOI4 in terms of combat. One can use things like projectile weight (the amount and type of bullets, shells) that can be calculated from the equipment table of a unit to figure out how much damage a unit could cause (manpower casualties and equipment loss), you can also throw in things like armor piercing capability vs armor as seems to be the case in HOI4 and also do the same type of calculations as a way of figuring out winners and losers. The direct fire support units could throw in their projectile stuff as well (i.e. an 88 mm AA bn probably increases the armor piercing capability of a division as does a battlalion of tank destroyers with 75 or 105 mm guns). Recon units could reduce the chance of "being surprised", engineers increase movement rates (or decrease penalties) for units with them as well as reduce penalties for attacking hardened positions or crossing rivers. Supply units could be highly valued (allowing closer to 100% of the unit to actually fight, improving movement rates), medical reduce attrition and combat losses, MPs again allowing the unit to be closer to "100%" in a fight. Unfortunately, I just don't know for sure what the developers have done with each type of unit or how they are actually resolving combat (my ignorance is clear but I don't know if I missed key entries in this forum or the information just has not come out).
