1. She might understand what you mean with "Was this a table", but you could also say "Did this used to be a table"? "Was this once a table" I think is correct, but "used to be" feels more natural.
2. I would say "He's an old friend of mine." "He is my old friend" might imply he is old, which you wouldn't want to say out loud :) You wouldn't say "he was a teacher" unless you are sure he is no longer one. You can say "Last time I saw him, he was a teacher". I would put a period, not a comma, between these two parts, since they are very different.
3. I would say "where did he go?" You could also say "what is this?", and the audience will probably understand you are asking out of surprise that he's a rabbit. "Who was this" doesn't make sense here. "Who" - you are asking about the person's name, occupation, purpose, but that's not the focus. The focus is the type of creature - human or rabbit. "Was" - you are talking about the tiny person, but it's not clear why when the audience is looking at a rabbit.