Can my father adjust status?

He should be fine. They let him in. As long as he did not misrepresent any information you will be ok

How do priority dates work in this case?

No you cant do anything now. until your dad petitions for you. when he does it will be by whatever your category is. so you have to wait till...

As a United States Citizen, can I help my father get his green card?

I highly recommend that you contact an immigration attorney. there are options that you have.

About i20 termination

its all terminated you received your f1 based on an approved I120. at least that what im getting from your statement

H1 B petition denied

what do they mean wrong client information? please explain more clearly

Can non-ctiizens receive disability benefits?

what kind of benefits are you talking about medical or financial?

If the divorce happens before the case is adjudicated then the kids will probably get denied.

Do my parents need 245i

No your ok to file for them with out any extra forms.

Resident tax for F-1 visa student?

what happened to your green card when you were a child?

Can i adopt an adult relative? will this help him gain citizenship?

You should consult with an immigration attorney. to see what your options are.