How should I pursue my mother's Immigration case with NVC?

They, and not you [unless you are an attorney] should contact NVC by phone or email and ask the status.

Need advise : If I join employer C full time on my EAD ,if my H1 is approved with COS for employer B what are my options?

Employer C should be able to do an H1b transfer.

I received my citizenship through adoption 10 years ago

No.

Immigration to USA

Not necessarily, since Canadians are not admitted for any set amount of time. Only recently as USCIS contended that they are admitted for only six...

How do you get in touch with Immigration to find out why an inmate is on hold and for how long the hold is?

Why is he on hold? ICE will put a hold on someone because they are in the U.S. in violation of the law, and is subject to removal.

Keep following up. If you wish, you can hire a lawyer to file a mandamus petition in the U.S.

If it is not given to you as a gift, but it is a loan, then no, it is not your money.

You can withdraw it. You do not get your money back.

Can I still finish out working on my J-1 visa while I submit and wait to adjust to permanent resident status?

Marriage does not violate your J visa status, nor does filing for adjustment.

Apply for a K-1 Visa while in J-1?

You would not change to a K1 but you would get the K1 outside of the U.S. Instead of getting a K1, you may wish to get married and file for...