Company denying pto before resignation

I have found a new job and told my manager and HR about my resignation notice (37 days).
Once I work there for over 3 years, I would like to have a smooth transition so my reference letter for the next job is not trash, but also want to use my 16 remaining PTO.

The company said that will give me five days of PTO (the very last week of my 37 days period) only.

I would like to know:
A. Is the company allowed by law to choose how many days I can take? If so, where can I find official information about this topic?

B. Will it be illegal from my side if I take the PTO anyways (saying that I am sick) after handing over my tasks to my other colleagues?

Thank you, guys