Can I travel through airplane within the U.S with an expired employment authorization card while renewal is pending ?

Your EAD must be current. If you applied for a renewal, you may have an extension in the receipt notice, and could possibly use that.

Lost job in L1-B and H1-B still pending for approval

If your H1 visa is approved, then you may get another job. These are questions best answered by your immigration attorney.

Application submitted to extend/change nonimmigrant status from current employer?

There is no reason to abandon the existing application.

Can I leave US without the result of my I539 application? Or is it better to wait for result, even after the requested date?

You can wait till February 2021 before traveling OR filing another extension request.

How do I send an indegent form for traffic tic from 06-07

You should consider consulting with an experienced traffic ticket defense attorney to help you on this. Alternatively, call the court clerk.

Ideally, you should file both together. You should consider privately consulting with an experienced immigration attorney.

You should consider consulting with an experienced immigration attorney on this issue.

Possibly. It's totally up to USCIS. They may use your old biometrics if it is still valid.

You can travel within the U.S, with a pending I-20 transfer.

Follow the instructions. You should look in your email as well. The notice might come in electronic form.