Can't have p.p. vs. couldn't have p.p.

I think I say "couldn't" in this context more often than "can't". The two are virtually identical; however, "can't" is more objective and concerned with the laws of logic, I would say.

"He can't have seen the movie" sounds like a detective's remark, a logical deduction from other evidence in the case, and so does "He must not have seen the movie", another equivalent! .

"He couldn't have seen the movie" sounds more everyday, and slightly more tentative (or conditional?) in view of the fact that "couldn't have" can mean "wouldn't have been able to". "would be" is always more tentative than "is".

That said, you will hear all of these in various contexts. They all say that it is not possible that he has seen the movie, or that the only logical conclusion from the evidence is that he has not seen the movie, which amounts to practically the same thing.

Your other pairs of sentences can certainly be analyzed in the same way.

No, it's not just weird. I imagine that most speakers feel "could" is more appropriate than "can" in sentences which refer to the past explicitly, as in "last year". Personally, I think c. is a possible answer as well, but as I said, it gives the impression of emphasizing the logic of the situation. "I can't have read it last year. It wasn't even written until last month!"

For test-taking purposes, "couldn't" certainly could be considered a "better" answer without being the "only" answer.

Please understand that others could have a different approach to your question!