Well, like I implied earlier it is probably just one component failing. And it might not be your power steering pump, there are several other components it could be. The serpentine belt in our cars has a lot more grip than the old V-belts, so a component has to really lock up to slip the belt. And it may slip for just a faction of a second, making it hard to catch early on. Also the fact, it is just one belt whipping around 6+ components, compared to the old days of like 1-3 components per belt. When a component hasn’t fully failed, it can be very difficult to find.
Also, just on a side note. I doubt anyone here can answer your problems 100%, specially your starting problem too. You seem to do all the regular maintenance stuff well, but it also seems to me you have been letting issues build up on your car. Regardless of that, if you don’t even know how to take off the aux. belt just take it to a garage.