Welcome to PPRuNe theflyingjapman,
I'll speak from what I see from the flight deck. I know I don't have the whole picture, but this is what I see from my window!
1. It doesn't seem to happen all that frequently. Typically only with IROPS (Irregular Operations). Therefore, expanding the math to all the other Captains, I'd say it would have to happen a couple times a week, expanding to a lot more during those IROPS.
2. Not normally at our outfit, unless the delay is extreme. The way the world was described to me is that someone in our OCC (Operational Control Centre) will look at how many passengers will be affected by the delays. The more passengers and their connections that will be affected, the more likely ops will try and organize a tail swap. Otherwise, for small delays, they won't bother and will focus their attention on the larger operational concerns.
3. Mixed. If there is an IROP that occurs and a tail swap is done, we simply have to update the flight plan and do another security check. However, they do try and leave those swaps for the first or last flight of the day to minimize the delays caused by the paperwork.
4. We almost always fuel with passengers onboard. With that said, we take a lot of different safety precautions that, if not met, mean we cannot have passengers onboard. It would be near impossible to operate a LCC or ULCC if we had to wait until fuelling was done.