this is my first question. My background is some analysis/calculus (In Europe it's a mix of both I guess) undergraduate course in an engineering college and a very very little knowledge of linear algebra and abstract algebra. I recently became interested in self studying mathematics and I decided to start from the foundations. I started studying axiomatic set theory and mathematical logic, and I have to say that axiomatic set theory is pretty damn hard, especially because there are no computations at all (as I'm used to from high school and college) and it's all about proving theorems over theorems. I've never learned how to do proofs, I was asked to do a few in calculus/analysis class but all I actually did was to learn them by heart and recite them (even though I could understand what i was writing, I had no idea why they worked etc.). Some of the theorems I'm asked to prove in these axiomatic set theory textbooks have proofs that make me think "there is no way I could have come up with that", some proofs are just too complicated, especially when I can barely follow along with the author (not only the proofs I mean in general). So my question is, what year is axiomatic set theory (or even maybe model theory since i plan to study it, mathematical logic etc.) taught in college? Is it normal for someone with my background to struggle so much with this subject? How can I learn how to write these complicated proofs? I've found a couple of books on Amazon, like how to prove it for example, but they teach techniques like proofs by contradictions, direct proofs etc. using simple examples and they don't really help much since sometimes to prove some theorems you have to think about some "crazy" tricks to do it.. so the obvious answer to this question is "practice a lot" but how? Should I try to prove a theorem in the same way the author proved it? Does this approach really help to learn how to come up with new proofs? Finally last question, are graduate students for example, required to come up with these complicated proofs out of nowhere? What should someone expect a graduate student to be able to do? I'm asking this last question because I can't really compare myself to anybody.
Sorry for the multiple questions, but I'm super confused and actually a little depressed since everything is so different than engineering and subjects and I feel like I will never be able to "fit in", especially since I have nobody I can ask to. Could you guys help me out please? Thank you so much!