Sorry for the additional post, but I didn't answer all your questions. I'm familier with my 824 with one belt, but things should be similar.
Separating the two halves is easy. It helps to have another person, but not at all necessary. I first removed the chute adjuster from the chute by removing the one nut (at the chute end), then setting the rod assembly out of the way. You may remove it in a different manner, just look at what would be easiest.
You also might have to remove something that adjusts the auger drive belt, I'm not sure.
Find something reasonably solid like a milk crate and place it behind the unit (under the handlebar area).
There are two bolts on either side of the unit near the top of the auger assy where it meets the drive section. Remove them, but be careful, when they are removed, the two halves can now pivot apart, hinged on a rod at the bottom of the unit (this is where the second person is helpful). The auger assy has a kind of notch that hooks onto this rod. This is where the milk crate under the handlebars comes in handy- to prevent the drive assy from tipping backwards.
Once separated, everything should be visible. Try and figure out why the belt fell off. Might be stretched. I would replace both belts while you're in there. The belts are not too expensive. Keep the old ones as emergency spares. I haven't replace the belts on my two-belt 824 yet, but re-attaching the auger belt may be a little trickier than the one-belt system when re-attaching the halves.
Good Luck
Ralph