I had a mosh connection open before I got on my last United flight and was able to use it the whole time. Seemed to me the free messaging/inflight entertainment tier doesn't block arbitrary UDP packets at all.
In general yes, but there are still some cases where mouse is better than the equivalent keys. Mainly resizing splits (guess how many lines you want and then C-w <size>|, vs just dragging the divider).
This was a revelation for me as well. I also didn't realize that if you haven't configured vi keybindings, the default is Emacs (in bash or anything using readline). Even though Vim's my main editor, I found modal editing a bit too heavyweight on the commandline, so I prefer the default Emacs (most useful by far: C-b to go back one word and C-k to delete everything right of cursor).