When Pressing P, you should add the server information to that area so that players can see what server they are playing on, to include name, Mode (1st/3rd person), Player Count, and IP Address.
Additionally, add "Add to Favorites" and "Remove from Favorites" buttons to this area as well.
N/A
Yes please!
This is a real pain when trying to remember what server you were on when the server reboots. You can find it by going into options menu, but it's a strange route to find that info. Normally on other games, the overall player/scoreboard menu is the place to find this.
I added this request (along with some others) back in 0.53, The request was passed over to the Devs. to see if it is possible.
The ticket is now closed but you can read it here 0021550