Hi. Thats a 3013 (P3) module (as it has 2 reed switches) with an oscillator chip installed where the crystal used to be. This means that at some point the old crystal has stopped working and someone has brought it back to life and put it in a P2 case.
On the downside your watch is no longer original, on the plus side it's no longer dead. If you paid a lot of money to a seller who should know better then it may be worth complaining but I doubt you'll get much out of it. These chips are great for those of us with modules showing "0", but they're becoming annoyingly common in watches sold as "most people would sell this as NOS".
The sensitive button could be an easy fix. Try covering the inside of the button (inside the case) with electricians tape (careful when replacing the module). If this doesn't do it then try alluminium foil and if that doesn't work then try swapping the reed switches round (hey, after all you've got a spare :D ).