1) Eventually! It's the end game for each prestige (only first 1 is really functional currently -- more coming soon!).
2) I went through great lengths to support mobile this time and it came at the cost of the desktop experience. I will improve this in the future -- I share in your pain.
3) I'm not sure if I have any control over this. It seems whenver the game is not in the foreground it stops working. I will look into this though.