I'm brand new the game and having a hard time with some stuff. First, plots only seem to do anything if it has over 120% backing which seems excessive.
You need to look in your intrigue tab, the same place where you have feasts, summer fairs and the like, and where tournaments appear. Plots make the appropriate decisions show at the top, sometimes with variety according to plot power/number of supporters (at least the claim-fabricating ones). You may sometimes indeed have no decision with >100% plot power merely on account of insufficient number of supporters.
Second, in my entire kingdom (Denmark) I can only raise just over 3000 levies which seems pathetically low compared to everyone else, thus requiring me to constantly hire mercs when supporting my allies Hungary and Poland.
It's possible the other dudes hire mercs too or have more land or higher crown authority. You may need to tighten your belt, upgrade the cash-generating buildings in your castles to enhance your income base (castle village => town => city etc., then wooden palisade => low stone wall => medium stone wall etc.), possibly jump-start your mayors (in other words get them a market or port with your royal money so that they start earning their own money faster and can start upgrading), get monastic schools in place when able (to support tech development, as they have the effect of a university while costing 1/3 of the price) with stress on your designated capital (the level of certain techs in the capital affects a lot of things). Marry your heirs well (meaning a queen regnant or a duchess with a lot of land for your demesne or a countess with 2-3 holdings if it somehow makes sense). When you have the cash, start upgrading your baronies but be economical about it. Basically think in terms of investment return. Get the lowest-tier troop-producing buildings first. Once it has begun to make sense, get the buildings which improve your levy percentage (wall does that, along with tax, by the way, although by a small margin but then a wall isn't normally expensive). If you want to play with your cultural buildings make sure that your own culture doesn't change. This means being careful about two things: 1) tutors, 2) landed wives (for which reason it could be worth it to give your son a barony just before "betrothed can marry" hits). Or else cultural buildings disappear when culture changes.
Income is extremely important here, whether you want to upgrade and rely on your own troops, or rely on your mercs. Monastic schools are important because you can get them early and +20% tech bonus for much of the entire game is great to have. A lot of technologies improve your troops and also a lot open new buildings (means you get to build your cash-generating upgrades faster) or increase the size of demesne you can have without negative effects, or improve your rate of gaining prestige or piety. Gold and tech are great things to have. If you handle it well, it's possible for a one-province ruler to challenge the King of England and win, for example. Denmark is extremely well predisposed here because it has ports everywhere. One's hard-pressed to find a Danish province that isn't a port. Ports make your cities richer. Just don't give in to the temptation of holding cities yourself: a mayor gets bonuses and all, with large taxes you probably get more from the tax he pays than if you held the city yourself--and, more importantly, the mayor gets to keep all the cash after taxation, which (unlike landed nobility who have other expenses) he spends on upgrading the city. And mayors are very good at upgrading. Denmark can turn into a veritable powerhouse.
For the record, Brittany is a country very much like your own in geographical/economic terms. Your experience from Denmark will serve you well if you manage to inherit Brittany, plus, Brittany is a huge duchy that covers an entire de iure kingdom. Which means you can create another king title the moment you get that duchy (as long as you have at least three provinces there out of a total six, according to the standard 50% rule). You can keep the entire duchy in demesne if you feel like it or you can give it to a cadet you want to be powerful or anything. At any rate, the building & upgrading process would be similar. Just don't build any cultural buildings of your own if you consider giving the land to a vassal who may be of a different culture.
Third, Italy all the way to the alps (including Rome) is conquered by an array of Muslim nations.
It may still be possible for the HRE and the Byzantine Empire to take it back. This especially if Byzantines hold the line against the Seljuks and the Fatimids and if Christians in Spain win. It also opens ways for you as with Denmark you're going to have a large fleet eventually and you can make yourself rich enough to get some mercs too (army or navy or holy orders for those holy wars where you are the attacker). Same rules of being a coastal king apply in most cases.
Fourth, I've just excommunicated by the church thanks to Sweden for apparently no reason what so ever.
That happens. Sweden may simply want you attacked by someone or distracted trying not to be dogpiled. You need some piety to remove the excommunication. A vassal may get it done for you too.
Fifth, instead of fighting the Muslims the HRE is simply conquering all of her neighbors including my former holdings of lubeck and Holstein which I cannot take back unless I attack the the entire HRE.
That does suck. Restart and ally to the HRE?
There are additionally some other options for dealing with the HRE:
1) Gain a duchy inside HRE's de iure empire. That gives you eligibility for elections as long as the HRE stays elective. Probably won't win yet but...
2) If you actually somehow manage to swear fealty to the HRE (which will tend to require the acquisition of a kingdom inside its de iure so that you can switch your primary title to that other kingdom and then swear fealty), you just might be able to win the next election or the one after, being the largest power in there, especially if the emperor isn't well-liked. Might be different considering your foreign culture.
3) France or Byzzies should have enough power to offer you real help on more or less matching terms with the HRE. England might. Hungary and Poland combined too, or Sweden & Norway combined. You just need to send gifts to their rulers sometimes when they don't particularly like you (need high opinion).
4) Generally try to put your dynasty on the throne where you can, marrying duchesses and especially queens to your sons and brothers (and your own unmarried or widowed ruler), to expand your pool of allies.
Any advice, especially when dealing with the HRE as their is constantly kingdoms trying to break free but they eventually get squashed. Is there any way other than fueling dissent to support a breakup of the HRE?
Being allied to those kingdoms (so you can get involved), making sure they are allied to each other (this is painful micromanagement but you can sometimes broker an alliance for two kings without their participation, e.g. when you have their kids in your court).