Affidavit of support ?

Yes, you must include all past three years of earnings. You should use the adjusted gross income for this purpose.

Would an online calendar converter be enough evidence to prove a mistake on a birth certificate DOB?

I agree with my colleagues. Best to get the birth certificate corrected.

How do i refile my papers that has been rejected due to improper filing?

Best to have an attorney review the basis of the rejection. Likely it was not just the G1145.

You file three years after becoming a LPR.

It is always a good idea to have a consultation at least with an attorney prior to submitting government documents.

Can I apply for Citizenship depends on married while we are separate?

Based on information provided, you will need to file under the 5 year rule.

Can I apply for permanent resident in Mexico if I am married to a Mexican citizen??

For questions about Mexican immigration, best to consult with a Mexican specialist.

Do I need a lawyer to process the documents of J1 Visa if the the which accepted me does not have an international office?

Best to consult with an attorney in private to determine available options in your case.

Can I file GC EAD (I765) Extension and Advance Parole (I131) Extension Online to USCIS?

Yes you may do so online. Follow instructions carefully.

If you have an extension on the I751, you should be fine to travel, even with divorce.