As an F-2 visa holder, you may only engage in recreational or avocational "schooling."

L1B to H1B conversion

You can extend the H-1B beyond the 6th year if either one year has passed since the filing of the PERM or you have an approved I-140 at the time...

Can I re-marry while my I751 waiver (battered spouse) is still pending after one year from filing?

There is no rule disallowing you to marry even though you may have an I-751 Pending. Consult with an attorney.

My US citizen adult son will petitioned me for I-130/AOS as I came to the USA as B-2. I have not file taxes nor my husband.

Your son's affidavit of support should overcome any "public charge" issue for adjustment of status.

What are the risks of applying for COS from F-1 to J-1 in order for F-2 be able to work with J-2?

You must consider all of the pros and cons before seeking a change of status, which are far two numerous to consider here. Consult with an attorney.

H1B transfer advice request

This complicated question should be addressed to the immigration attorney at Company C or an independent counsel of your own choosing.

I-130 & warrants

The CBP will not permit your husband to enter the US to address his outstanding warrants. Consult with an attorney.

The Embassy can always run a background clearance check in association with any visa application.

TPS procedures after biometric

The EAD may take up to 90 days. if you do not receive an EAD by then, you can schedule an InfoPass with USCIS to follow up, or contact an attorney.

Conditional green card.

The USCIS could easily take 6-12 months to schedule an interview on a pending I-751 case.