Closet size depends on the aircraft. On most aircraft, the closet is for first class passenger jackets, etc, plus crew bags, but one folding wheelchair (assuming the passenger takes advantage of preboarding) has priority. My wheelchair is 15"x17", with 24" wheels.

You're unlikely to be able to determine for certain that your wheelchair will wind up in the cabin on any given flight. I know that's scary, and I know that you've had previous experience with your chair being damaged. We just have to take that risk into account. Be aware of your rights as a wheelchair user. Be polite but firm in requesting them, or in requesting something additional (like having your rigid chair stowed in the cabin). If your chair does wind up going under the plane, take everything off that could be lost or damaged (cushion, bags, etc.) Put a permanent label on it. When you get it back, check it for damage then and there on the jetway.