Applying for asylum post 1 year?

Deadline for Asylum is within 1 year, looks like you have passed that deadline, however you might qualify for relief under withholding, you should...

H1B Petition Denied, Can I Appy F1 Visa?

There would be a record of the denial, but it affecting your future petitions is speculative, unless there is a direct correlation.

Can i apply for visa through my father?

Yes, your father can petition for you.

Yes you can re-submit the entire package and include the rejection letter and the biometric fee.

What documents need to be sent to Immigration if a U.S. citizenship certificate is lost besides an immigration form?

It all depends on what you are filing. As mentioned above, you are able to file for a replacement certificate.

Naturalization

I might just be, like mentioned above, check the processing times in Dallas.

If my wife sign for deportation and her country of birth doesn't accept. Is there a way for her to be a citizen or get her green

I agree, it would not come out of the deportation process. Would need more information to determine if she can somehow qualify for green card, best...

If I was you I would familiarize myself with the USCIS website. I have attached a link below to check your case status. Houston does get backed up...