1) I don't think it's possible to keep the standard Ubuntu menu but you can use XMonad in other desktop environments like Mate or Gnome. You'll have to do a bit of configuration but it's not bad, see my other comment.

2) I run XMonad in gnome and it mostly works without problem. The only thing I had to change was set my browser launching keybinding to run

          spawn "google-chrome --force-device-scale-factor=1.4