The fan is there to remove odors and and grease that might fly up (though you can't see it most of the time). At 300 CFM it is not a very large fan, but it can be noisy for a lot of reasons.

As for using it while the oven is on, it is not necessary, but some people do it. My oven, which is a stand alone wall oven, isn't even under my range top so it is no where near my hood.

Also, most times, the OTR micro-hood combo's don't vent to the outside, they can just be a recirculating version. I had one in my townhouse, and it did vent to the outside, so it could be, it is hard to say without seeing the back side. Though you can put your hand in front of the unit near a vent and see if it is blowing air back into the room when on, if so most likely a recirculating vent then. At that point make sure you clean all filters for it to operate properly and do the best it can.

As for do you have to have it going, no, not at all, it is personal choice, there are people that have no vents at all over their cooking area's. Gas doesn't create enough fumes to worry about as long as it is burning properly. If you smell gas while cooking or using the oven you might want to have that looked at though.

Phil