After the belt broke, it could have gone to many different places. it could have broken away and slipped under the car, harmlessly falling to the ground - that's the best case scenario. Sometimes they will wrap themselves around things like a whip.
It could get trapped under one of the pulleys and subsequently ground down. when this happens, you'll get a burnt rubber smell that goes with that.
After the belt breaks, you immediately stop losing the alternators ability to recharge the battery (along with power steering, air conditioning with a serpentine belt). When this happens, you only have the amount of power that the battery had in charge when the belt broke. So at that point the cars electrical system is running on battery power ALONE. If you continue to drive the car after wards the battery loses it's charge, so things like using the starter or turning on the radio with the volume up loudly has a tendency to drain the battery ALOT faster. and the car is still using the batteries power to run things like the engine computer and it's accessories.
As far as the Q regarding how long the battery will last : Who knows ? Mostly it depends on how much the battery was charged up at the time the belt broke. This can be a lot or a little and battery age will effect that as well.
A jump start will not recharge the battery. It will only provide enough power to get the car started, as if you were using the other cars battery for that moment. When you remove the cables after the jump, the original car (with the dying battery) is running on the dying cars battery AGAIN.
The moral of this story is that the dashboard light that came on (when the belt broke) should let you know that there's a problem with the engine.