1. Yes, an option for this could be added.
2.,3. I already though about this, but your post speeded things up and now its implemented, so it will be in the next release.

Great software, here are some things I thought of.

1. an option to stop the splash screen (I use this at work and that splash screen makes it rather obvious that I am doing something I shouldn't )
2. tooltip in the tray icon showing track information for the song the player is currently playing
3. controls for the internal player on a popup on the try icon (so I don't have to restore the whole app to pause/skip tracks/etc.