In most (not all) cases, the bezel's inside diameter is a bit too small to fit a gen xtal. So you will probably need to enlarge the inner diameter (with a Dremel, round file, etc) to fit a gen xtal.
As explained in the thread, the hour totalizer was running even when the chrono is off. As I recall, it was due to a worn braking component, but you (or your watchmaker) would need to disassemble your watch to diagnose.
No need to send me pics. Without having the watch in front of me, there is no way to ID the xtal or case. But feel free to post additional pics here (in the forum) in case another member is able to see something that I cannot.
Impossible to tell the xtal or case from the pic, but the dial (which looks nice) does not look like it came from DW (not sure what it is) & the coronet does not look it came from Rolex.