On my van, I have a 12V 100Ah battery.

Let’s say I have a 100W hair dryer that I run through a power inverter. For how many hours can I run it, before the battery capacity ends?

The formula to use is Wh / V, which in this case means

100Wh/12V = 8,333Ah

1 watt-hour is 1 watt of power expended for 1 hour

Since the battery is 100Ah, I can run it for 12 hours (100Ah / 8,333Ah).

If I had a device that consumed 200W, I could run it for 6 hours.

This assuming the battery is 100% and I can consume 100% of its power, what almost happens with a LiFePo4 battery, but not for regular lead-acid batteries.