If the sole basis for the finding was your CPT, changing to another university may not necessarily help. If they don't believe you plan to return...

No, it is unauthorized employment and in violation of your status.

Should be, but of course there are never any guarantees.

There is a traveler redress program, US TRIP. Other than that, you would have to file a lawsuit.

Your current, unexpired visa will allow you to be admitted to the U.S. Discuss with your lawyer what other documents you should be prepared to...

The consular officer is permitted not to believe her. As such, I suggest instead to have her son file an immigrant visa petition for her once he...

No. Your child will need to wait for five years from getting his or her green card before filing for naturalization.

No, you are still a permanent resident even if CIS approved an H4 after you got your green card.

It would be a good idea to wait before filing, to avoid any allegation of fraud.

If you have questions about CIS' e-filing, you should contact CIS customer service.