Ca in employment

ya a CA can be a director in private ltd. 

and yes A pvt ltd can be there without any employees..... i m having companies under me doing the both point as u said above

There is required to intimate the Institute....

Yaa of course he can be a director. I don't think it is required to inform to the institute as he is not in practice.

Regarding formation of private compay without employees, there is no any restrictions in Companies Act.