Are my three questions grammatically wrong?

I have written down a few questions below.

(1) Is there free parking for staff? (my colleague's question)

(2) Is there free parking for the staff? (a possible question I would ask)

(3) Does the company have free parking for staff? (a possible question I would ask)

(4) Does the company have free parking for the staff? (my question)

I am a new employee in my current company. Last week, I asked my colleague about free parking.

I used (4), and he rephrased my question and used (1). He is a native English speaker. For sure, his grammar is excellent.

Are (2), (3) and (4) grammatically wrong?

Thanks a lot.