The Employer's lawyer should be preparing you for any interview at the Consulate.

My h4 EAD expires on December 13 and my application for renewal is pending with Nebraska center can I any ways expedite this

You can always request that the application be expedited by contacting Customer Service.

Immigration law question regarding H1B transfer from employer A to employer B

The change of status will not be approved if you have not been maintaining status according to the terms and conditions set forth in the LCA. ...

How easy is it to get a university H1-B visa given current immigration trends?

You need to have a willing sponsor and a position that qualifies for H-1B status. Consult with an attorney for specific details.

What would happen to my current work permit if I file the VAWA waiver?

You will be able to renew your work permit as long as you have an I-485 application pending with USCIS. Consult with an Immigration Attorney.

Status on H1B when visa is expired and new I-797A is not received?

The I-797 is evidence that a Petition was actually filed. You must obtain such evidence, otherwise it could be that no extension has been filed...

Is it possible to extend a tourist status even if you came to the country under a j1 visa?

Possible, unless you are subject to Section 212(e) and still difficult if you are not.

This is not an immigration question and should be addressed to a DUI lawyer.

Consult with an attorney in New York who is experienced in Federal Litigation involving overdue USCIS benefits. Fees will vary.

H1B 60 day grace period only available if one has valid I-94?

You would be considered out of status and ineligible for an extension of status.