Ok, first of all congrats on the new friend.

Now then... next time, offer the mouse WITH TONGS. Holding it by the tail is just asking to be tagged since you are warmer than the rodent.

A sated snake will curl up in their hide (usually warm side) for a day or two to digest. Some snakes will lay with their heads out, so that's not unusual. If he were actively searching around, he would still be hungry and seeking more food. Of course, I defer to the more 'in the know' people on that one...

What size mouse did you give him? It's best to offer a prey item that is about as big around as the snake's widest part.