1. Can I say that the PIC works beyond the clock specification? For what reason does it work?
No device will stop working the moment you overstep a design limit.
However, the moment you do, YOU are responsible for any obscure failure at the limits of supply voltage, temperature etc.
2. If I can operate at frequencies beyond the specification, what is the possible maximum clock over the specification?
Impossible to predict.
This will vary by chip batch, supply voltage, and temperature.
3. What are some of the problems that can be expected or unexpected when using frequencies over 32Mhz?
Failure to work as specified in the datasheet.
No-one can predict exactly what or where the failure will be.
If you choose to exceed the maximums listed in the datasheet, then it is YOUR RESPONSIBILITY to fully test the device under all possible conditions to ensure it still works reliably.
(Note, this is simply not feasible for most users)
Bottom line, exceed the manufacturer's specifications at your own risk.
If it's a one-off, sometimes you can push the limits.
If it's a commercial product, I hope I never buy any from your company.