I-765 renewal if outside the country ?

Possible but unlikely given possibility of biometrics.

Your father would need to file form I864 and you I 864A as household member.

An expired passport should be sufficient to establish your status of US citizen for such filing.

To obtain a legal citizenship is marriage the best option out of the others?

Family-based immigration is an option depending on your particular circumstances. Best to consult with an attorney about your situation.

I sent all the civil and financial documents to the NVC. Last week got an email that my income is not sufficient.

You may want to consider a joint sponsor rather than using your savings.

Naturalization: We are taking longer than expected to process your case. You do not need to do anything at this time.

Unfortunately there have been significant delays with interview scheduling due to Covid.

You should answer affirmatively and provide explanation for the incident.

No applying alone does not invalidate the visa.

No, divorce should not impact your residency.

The original Soviet union birth certificate should be sufficient however best to discuss with your attorney.