You restart the first floor over and over and over and over until you have an item room in the first room and said item room contains something workable. Then you hope that first item is enough to carry you through 2-3 floors while you build up through mostly devil deals. Dead Cat is a big deal.
All you need is a powerful build, really, as avoiding damage obviously gets easier the more powerful you get. The further you get, though, the more you kinda have to have Dead Cat to avoid bullshit damage.
Rotten Baby does not deal garbage damage and the idea is for you to center your playstyle around him, not the other babies.
It does not. I would uninstall the game if it did, that would be the final straw. Angel rooms suck so fucking bad.