I have a PhD in Computer Science. I need to apply for the GreenCard and not sure which category I fit in

You would likely fit the EB-2 category, but it is a complicated process and you would be wise to use services of an immigration attorney.

Issuance of driver's licenses is a state issue, not federal. So it will depend on the rules of your local DMV. You can try requesting a new license...

What is the fastest way that I can bring my child with me here in the U.S.A?

There is not enough information to answer you. It depends on your current status. You should see an immigration attorney as soon as possible.

No, your husband is not eligible to apply for SSN or a work permit.

What's illegal for a 14 and 21 year old to do over text?

You shouldn't be communicating to a 14 year old. Just stop writing any text messages to the minor.

Can I sponser a friend from mexico for citizenship

You can do it if you have enough income taking into account your other dependents. But before doing it, carefully consider that you would be on the...

Am i obligated to pay This Back?

Yes, unfortunately, you will have to pay back the amount they overpaid to you by mistake.

I-130 Approval

I-130 approval date does not have anything to do with the priority date for your immigrant category. I-130 is a necessary step in the process.

Unfortunately, the asylum process takes a long time. It could even be several years.

Am I required to stay with an employer that sponsored GC for me?

No, when you have your green card, you do not have to stay with the employer.