How long will a 32v 15A (500Wh) e-bike battery last outputting at 5V 1A?
1) Around but less than 4 days (500 Wh / 5 W = 100 hours = 4 days). Because the conversion efficiency is less than 100%, you will not get the full time.

2) it won't hurt the battery itself but who knows what the 5V circuit will do? In any event it is not adviseable to exceed the limits of the stuff you buy unless you are willing to take risk. Most likely outcome is that the 5V output will be shut off by the battery pack.

3) This should not damage the battery. It may be difficult to find such a circuit. Basically you are looking for a 32V inverter. Maybe a 48V inverter will work.