Transfer Reason

I think Yes.

One of the clauses which allows you transfer is -

• Transfer of a working parent to another city involving a distance of minimum 50 kms (on production of a certified copy of the transfer order and the proof of relocation to another City).

Your case will be covered under above.

Yes. u can get transfer. U just need to submit ur father's transfer certificate alongwith form 109. 

My father is not transfered, but he had left the job

I think main provision is regarding movement of family from one location to another as aresult of which article wont be able to continue under his present CA.  Hence transfer/resignation should be treated equally.  You should apply for termination.  If institute will have any objection they will convey it to you.