Just sign and resend with green sheet by certified mail, return receipt required. Make a copy for your file as well.

Can I work full-time CPT 40 hours while Spring term?

As long as your school approves, but be aware that full-time CPT will eliminate your eligibility for OPT.

Adult adoption is legal in NC but your overstay means you are acquiring unlawful presence which could be a bar to re-enter or remain in the US...

In the past, I have seen this arrangement work as long as it is a bona fid marriage with ample proofs, particularly familial (children), financial...

I got married to a girl in December and she filed her I 130 through her father who is a citizen in November, So 1 month before?

Her father is a US citizen; you are not. It sounds as if you are an F-1 which might entitle her to F-2, which will end when your F visa status...

Parents visitor visa, offboarded from plane denying entry to onboard from start location

File a FOIA request and then determine if legal assistance is warranted.

Can I say "NO" on my I-485 for Being arrested since I had my record expunged?

Disclose everything and you cannot be accused of fraud or misrepresentation which will sink your case.

If I 751 denied can I re apply or go to immigration court, which one is faster?

To determine if the reason for the denial can be overcome, you need individualized legal assistance. This forum is too generic for such purposes.

What evidence of her physical presence in the US for 5 years could she provide besides leases and tax return transcripts?

I agree with my colleague. The USCIS has access to CBP records anyway showing departures from and returns to the US.

What lawyers in North Carolina will help me get a visa to go to Algeria to get married in Algeria

A NC lawyer is probably not licensed in Algeria to know the law there so of course you cannot find someone local here in NC. You have two...