No Micro, I think you really are misunderstanding the game mechanics. The AI does get a few bonuses, but frankly, I would put that out of your head completely, if it's leading you to think they have teleporting units and special exceptions to battle mechanics or diplomacy. Blaming your own mistakes on the blanket assumption that the AI was cheating just means you're never going to understand how the game mechanics actually work, and until then, will find the game needlessly frustrating.
I really don't see how England disliking me has anything to do with the French abandoning their war with them and then having England ally with the papal states (who were at war at the time and miles away, I know if I tried that I would never be able to ally them).
England has loads of troops and was still catholic. If they're catholic, they'll improve the papal state's opinion of them, and if they have loads of troops, they can ally with pretty much anyone they like on the same continent (distance between borders matters much less when making alliances than it does for marriages and diplovassalizing). While the Papal States is in a defensive war they'll get a -50 acceptance malus when
sending alliance offers (-1000 is when sending alliance offers after starting an offensive war, and the AI gets this just as the player does), but no such malus when judging whether to accept an offer
from someone (such as England). This is exactly how it works for the player, and if you kept a save and tag switched to England you'd see that the Papal States would gladly accept an alliance from England, even if they hadn't improved relations. They may have even accepted it while England was still in their war, but probably not unless they were really hurting. Just playing the game normally this should be obvious, and as the player you can also make new alliances and call them into your defensive wars after the war has started (normally players don't fight many defensive wars though).
If you don't want to fight the Papal State's allies, don't make them a cobelligerent. It has never been more clear to the player in the history of EU4 or EU3 as it is now how alliances will be called when declaring war, and the player has never had as much information or options. If you're declaring wars on people, check the opinion mapmode on the target to see who's "friendly" with them. It takes like 10 seconds to scan over their neighbors and people you don't want to fight, and will prevent you from making this same mistake again 95% of the time.
France peacing out with England without taking anything (or only taking one or two provinces) is very common. England starts as a hugely powerful nation now with loads of development, and likely had allies in that war with France (since the war isn't going at game start in the newer versions), so even when France occupies all England's continental possessions, they're unlikely to get the warscore to demand much. AI France probably peaced out after getting full ticking warscore and after the length of war modifier reached a certain point, in addition to whatever other factors (like manpower, WE, or if they had other wars going or revolts).
I CAN agree with that. Some of the stuff the AI gets away with is utter horseshit.
Like what?
Here's a complete list of AI bonuses, still valid for this version.