Can I change status from O-1 to F-1?

Yes there are no prohibitions on changing status that way.

You need to provide the grounds of inadmissibility (criminal record, immigration fraud, etc.)

It may seem silly but they really should be printed on only one side.

What the chance of reinstatement after this long period?

Your DSO will be able to help you but normally reinstatement must be completed within 5 months.

Can I get a new J1 visa it hour completing the HRR under my old J1 visa?

Does the post doc position also have the 2 year requirement?

How can she stay here without a sponsor

There are few ways a person can live in the U.S. such as being a student, being sponsored by a USC or LPR family member, or working for a U.S....

Will my bad credit history prevent me from obtaining a H1B visa.

On those facts alone you should still be eligible but was a judgment entered against you that you did not fulfill?

Can my wife enter US while my petition is still under processing? What documents she have to carry at POE?

She should be able to - just make sure you give her a copy of the H transfer and your recent paystubs.

Can I legally stay in rented room and withhold my rent until I get a proper notice to move out?

Withholding rent is called self-help and is forbidden in 99.9% of circumstances.

Can she sue me or do I really have to pay the rest of therent

Remember you landlord also has a duty to fill vacated place.