Same as the H1b itself, except that the labor condition application and wage request are for the new location.

A pending PERM does not prevent one from being issued an H1b, or being admitted to the U.S. on an H1b.

A photocopy of your passport will be fine.

They may not be willing to issue a second EAD, but perhaps so that you can maintain your F1 status you should file.

Did they pay the visa issuance fee? If so, try the CIS website and send an inquiry by email.

Tell them to file an application for a tourist visa.

Assuming there are no other errors and that the forms are not expired, and that your parents status is not expired, you should be able to do that.

Follow up with USCIS Customer Service.

You get a six month extension of your EAD in the c8 category.

As long as you are still receiving mail at your current address it is not a problem.