Can I say,

The owner of the car and the policemen thanked me because of help / helping them (the police) to arrest the thieves.

My parents were pround of me.

(b) The policemen praised John of his quick thinking brain.
Because of helping.

I wouldn't use "because of". Say "for". The policeman thanked him for helping....
Teachers: We supply a list of EFL job vacancies
HOa bout (b)? Is that correct?
I wouldn't say quick thinking brain. I would say "quick solutions" or for his "being quick".

By the wat don't forget this: praise someone for something.

The policeman praised him for his being quick.