I looked at myself in the mirror. She looked at me.

I have decided to just be myself. Kind of an odd case there.

I, myself, love to go to the movies. Here it is just used for emphasis, not as an actual reflexive pronoun.

Some people do use the reflexive pronoun as an object in certain cases, often with compound objects, but it is not proper under any prescriptive English grammar that I have studied.

I assure you, "it's me" is in far more general use than "it is I". The latter, and the purported rule that copular be takes two subjects, is at best exceptionally formal, and many English-speakers don't readily produce it in any context. Quick litmus test: check how acceptable the equivalent constructions are to you for "us" vs "we" or "them" vs "they": "The only ones who got it right were they."

And then conjunctive compound NPs are clear as mud; you routinely run into otherwise impeccable speech where the governing rule seems to be that local euphony trumps long-range syntactic agreement. There's no good prescription here; there's a pretty wide range of pronoun conjunction constructions where you're going to want to either rephrase or just suck it up and let it sound intuitively wrong to somebody.