You can petition for her as a fiancé showing that you have met her within the past two years. Consult an attorney for more info.

As you will be getting paid, it would be considered work which you are unauthorized to do on an F1 visa.

Will the court report me to immigration for getting arrested driving without license?

It all depends on basis for stop, if an arrest was made, and how it will or has been ultimately decided. Drug possession cases carry significant...

Should an Iranian individual wait to apply for a green card until after the immigration/muslim ban is lifted?

It should not affect eligible green card applicants, only visa entries and for a window of time. I think you should be okay to apply now.

It doesn't appear that you lied but advisable to meet with an attorney to confirm that you are not committing any misrepresentation.

Violation of term of visa, any chance to reinstate the visa?

If you are eligible to change status then it is advisable to do so if you are not complying with the terms of the visa. However, speak with your...

No you don't need the A listed and in the case you don't have one, simply indicate N/A.

Can I use my nigerian court certified birth certificate for AOS? Do I need to translate it since it is in English

Yes since it is the official birth certificate. Also no need to translate it if it is in English.

Greencard

Unfortunately no and accruing unlawful status can have significant negative consequences. Consult counsel for more info.

Family Based Immigration - I-130 Filling for unmarried over 21 year old child by LPR

Yes, she can apply and she will also need to provide birth documents.