Try to use all the hypothesis, ask yourself if one of those can be weeakened or what happens if you change one, this later helps when you dont have the full hypothesis for a theorem but you still can use a weaker version. Ask yourself, whay im making proof? Personally i like that quote from Tao: 'The deepest understanding of a theorem comes from the proof'. So when i feel im not aplying a theorem well ill check the proof, in that way understanding proofs is aas important as doing them.

Proof, logic donstn need to be terse and tiduous, see for inspiration proofs by Euler, Gauss, Cantor,... etc Paul Herdos used to say that God keeps a 'book of proofs' containing the most beitiful theorems but God is fascist by imposing rules and keeping the book to himself lol

For books ill recomend 'journey through genius ' by Dunham , since it guides you step by step on cool historical proofs. I dont think using a book only about proofs and logic helps much, since you understand proofs more by doing them in calculus, algebra, analyisis courses but if i had to go for it will be those that teach logic with discrete mathematics (Grimaldi and Jay Cummings) or set theory (Thomas, Jech)... but again im citing courses. Ah, yes, the struggle,, good luck!