Others have already answered your question well, but I want to add something about #4, the mathematically more serious mistake. Since by your own admission you are inexperienced, I can see why you spent three evenings trying to repair the proof, but I personally would never spend that much time in such a situation. In my report, I would simply say that the proof is not acceptable in its current form because claim X is insufficiently justified. (I would also keep going through the proof under the tentative assumption that claim X is correct, to see if there are any other issues later on in the proof.) Say that the author must either provide more justification of X or find a way around it or retract the theorem. In one case where I did this, the author did indeed retract the theorem (it was not the main result) because he was unable to repair the proof.
Proofs are supposed to be verifiable by competent readers with only modest effort. If you're qualified enough to referee the paper then you should not be working so hard to understand the proof.