As you stated before you went home to get a visa for your F-1 status; you did not change your status. The same thing must appen to obtain O-1...

Will USCIS consider me ineligible for sponsorship for acceptance of temporary snap and Medicaid?

That will certainly raise concerns since you must show sufficient income to support your father.

Can I take the affidavit of support to the US office in Irving Texas now or wait til the waiver is approved?

the affidavit of support should be prepared and filed withe US consulate in Juarez as quickly as you can.

What will happen if my wife goes to court?

If you mean a court date regarding the ticket more than likely nothing will happen regarding her immigration status.

My Case is very difficult, it's been only a maximum of 8 months for me in America and married.

Unfortunately proving temporary intent is difficult and under these facts will probably never be possible.

Do i have to mention my speeding ticket and changing in wrong late ticket during my citizenship interview?

Yes you should and they should be listed on the N-400

I assume you mean I-864 and you cannot withdraw it. You are always liable unless your spouse becomes a US citizen or works for ten years.

Q1: Can I file VAWA Q2) should I contest my marriage annulment to convert it divorce in the court so that i can file VAWA.

I am afraid you are looking for easy answers to a complicated situation. Even if there were "VAWA experts" that is unlikely to be an option let...

Employment based Greencard when husband is a US Citizen

There are advantages and disadvantages to each option which you should discuss with tha immigration attorney you already have. Also note there is...

Will I be able to apply or get approved for OPT , if I've used TPS based EAD during my F1 status & maintaining fulltime study ?

As long as you have maintained proper F-1 status and NOT used the TPS for work, then you will get all of your OPT after graduation. This also...