Is it all right to switch between the different types of gases at each use? Will it harm the stove?
It shouldn't harm the stove, but you will see various degrees of performance. Try to avoid unleaded gasoline if at all possible. I would stick with white gas (ie. coleman fuel) whenever you can. White gas is the cleanest and best performing fuel with the highest BTU rating per ounce than any other fuel type. The true benefit of a multi-fuel stove is when an emergency situation bears it's ugly head. It's also a benefit if you travel outside North America. Other than that I would stick with white gas.
Au contraire! Both white gas & kerosene max out @ 10K BTU's whereas isobutane/propane blends increase, at last count, to 24K BTU's. Granted stove design & gas compression do contribute overall, but you won't get as much heat out of liquid fuel @ this point in time!