1) correct. You don't have to vote in *any* catagories, just as long as you send in your 'vote' on time.
2) No
Your ballot doesn't have your name on it. You put in an envelope. Then you put that envelope in another envelope with your name on it that you sign, right? That's how it happens in Oregon. Here, the first envelope is received, noted that you've voted, and then the inner envelope is thrown into a pile (perverbial). Then those are taken to a counting center and opened and tallied.