Questions about Divorce Laws

Is it possible to file divorce while staying with wife? If not, what's the alternate?

Yes, you can file for Divorce while staying under the same roof. 

What legal action wife can take if husband leaves the house and starts staying away?

She can file for restitution of conjugal rights, for maintenance etc. 

Note- Husband and wife staying together since; wife is not allowing husband to move out and stay separately and keeps on harassing him mentally and physically both?

Husband has videos captured as a proof of cruelty.

Can he file the case on the basis of video proofs he has. Even if his wife is not letting him move out of the house and stay away?

Yes, he can.  

Marriage was solemnized in Punjab however; both are residing in Delhi due to their work locations.