You can absolutely 100% the game. The best you can do is 365 with 13 hearts left, but that would be the single luckiest game EVER, but getting 365 is completely doable. And no, the exp builds up and is usable until you use it.
Did you find the gnome? I wont spoil what happens but you need to find him.
Did you kill the Mine King? His scroll turns all mines into free exp