Based on the circumstance you describe you should be eligible 245(i) adjustment.

Can I work on current H1B for couple of week even my H4 COS and EAD are approved?

As of H4 approval you are no longer on H1. H1 employer must update their Form I-9 with you H4 EAD. No need to leave the US. Don't leave the US...

Transferred H1B to a new company and decided not to join them.

There is a memo that I believe is still good law permitting you to remain employed by an initial employer's unrevoked H1B.

Can my husband visit me in US on his valid tourist visa while his I-130 and I-129 (K-3) are being processed?

A person on a visitor's visa may be admitted despite an I-130/I-129K filed. The spouse must honestly answer questions.

Can I work if my L2 EAD expires but my immigration status remains same.

So, long as you file before your EAD expires the new I-140 regulation grants 180 days of employment authorization.

I have H4 EAD, I am planning to apply for F1 visa. If in case my F1 is rejected, will I lose H4 EAD?

Generally, H4 is not necessarily cancelled should the F-1 visa application be denied.

Can I legally stay in united states until my I797 expires though my VISA is maxing out?

The I-94 validity controls one's stay in the US not the visa validity.

Immigration Question - Green card and adjustment of status - F-1 status.

You remain on F status until the AOS is approved. Working on a pending AOS EAD will violate the F status. A person in F status may apply for and...

Travel during F1-Opt to H1B visa processing

Generally, a person in F status with an F visa may depart and return to F status when an H is pending or approved before Oct 1.

You have been "advised" to maintain a more permanent home in the US. Recording you have been warned to maintain your residence in the US. You are...