1. I think you can right click a chat window and close it via the context menu that shows up?
2. I'm not sure what causes this bug because it hardly ever happened to me. Try resizing your chat window vertically and switch between the options to try to correct it.
3. Yes, in the DrumsUI Menu (accessed from the stat bar)
Sorry, I haven't been playing in nearly 2 years, so I'm rusty on the chat window.