Can I apply for OPT or Stem OPT if My dad already filed a GC petition for me?

Yes you may apply for OPT or stem OPT.

You should try to maintain your F1 status. In the event you are unable to do so you may continue to take courses while adjustment is pending and...

Can I use my savings to qualify as a sponsor for my mother's immigrant petition?

You can try however it is likely you will be required to have a cosponsor. To avoid delay try to locate a cosponsor.

You may apply for positions however you may not begin employment until you have the EAD.

It may go to Detroit for any number of reasons. In many situations it is for further review and inquiry.

How can I renewed an expired green card that expired in 2015??

Apply using form I 90. You can obtain the form on USCIS.gov.

Can I apply for citizenship with an expired green card that expired in 2015?

Apply for your resident card using form 1-90 first.

H1B maxout convert to H4, leaving few days?

You should discuss with the immigration attorney that is handling the matter for your employer.

Employment outside of the duties as an au pair is not permitted.

What should I do?

A good place to start is to schedule an info pass appointment at the local office where you were interviewed. Depending on the results of the info...