1)
Drink restores mana
Food restores health
2)
health and mana restores while in the battle tower.
Mayby the fact that they do not is a feature or a bug, but if not here is a suggestion.
Imarion
food & drink already do that thay just don't recover a lot
& if thay were to allow you to heal in the battle tower it would make the game 2 easy as everyone would be travaling back to the tower everytime thay were about 2 die.