When is the game saved, and how?
I would like to play D3 in my lunch time, but I'm worried about one thing.
Is there a way to save my progress in the game, besides the check-points?
check-points are for quests only. As per your inventory is concerned, it's auto-updated to the server.
Diablo 3 is all saved as you go. You can leave and resume where you left off at any time.