It is recommended you select one method of application throughout the process.

Employer may sponsor a person's kids and is not a ground for rejection.

Yes, you can travel out of US with your H4 EAD in pending status, provided you meet all the H4 visa requirements to re-enter US.

Every single for submitted to USCIS must have a supporting document.

You may discuss with an attorney in private for your best options. It may be at your disadvantage to discuss your criminal history in a public forum.

Recommended you consult with an attorney to consider possible options for you.

Yes, it is allowed, he may sponsor you for permanent residency.

Your cae appears to be out of processing times, initiate follow up procedures. An Info Pass appointment at Tampa Field Office would be helpful.

His application may have problems. First, "Immigrant intent" and second, a student on F1 visa needs USCIS authorization to work. I suggest an...

Your facts may be confusing as well, as most people receive bills at their physical address. Contact USCIS with corrections or confirmation.