When you access a card from HQ due to a successful run (or any other reason), does the corp player get to see what card you accessed (assuming it wasn't an agenda and either was not trashable or you chose not to trash it)?

Hard to say. Obviously, being from HQ, you should be able to look at your hand while they have your card, and tell what is missing. But I don't think they're required to specifically announce what card they have. Also, once they hand it back, you should be able to tell.

I don't think the game forces you to randomize your hand, put it facedown on the table, let them access, and then replace the card back on top of the HQ, re-randomize it, and then let you pick it back up.

If the runner access the HQ (i.e. the hand of the Corp player), the Corp player would be able to know which card is accessed.

If the OP means the R&D (i.e. the draw pile of the Corp player), then no, the Corp player would not be able to know about the content of the card being accessed.