Do I need a new H1-B stamp on my passport

You do not need to get a new H visa only because of a change of employer.

Yes, you may renew your DL on the basis of the H-1B. As to the documents you need to carry, check your states DMV website.

Is travel document for domestic or international travel?

You do not need a travel document to travel within the USA.

Can i travel to US for personal work with H1B visa ?

You may enter on an H-1 visa only to work for an employer whose petition on your behalf was approved.

How long can I work with my L2 visa when my partner has a L1 visa with PED in one year, and expiration date in 5 years?

You may work on the basis of an L-2 status & EAD for as long as you maintain that status - which is as long as your spouse maintains L-1 status.

Regarding H-1B extension and recapture eligibility

you say "H-1B beyond 6th year can only be extended if my PERM was filed 365 days prior to my H1B expiry date" that is correct. Given the nature of...

I am out of status here in US. A person who is in US on H1 wants to marry me and apply for my H4. While I am here in US.

No, one cannot apply for a status change, when one does not have any status.

I am on H1 b visa and on maternity leave for 6 months now and wanted to join back but my co is not doing well financially

The solution is dependent on several factors of a sensitive nature - so you should consult with a knowledgeable attorney, in person.

Out of status- missing payslip for one month , cause my h1b Transfer RFE rejection?

You should discuss this with the attorney who is handling the RFE response, since the answer and solution depend on many factors.

New I-797

If your H-1B is not revoked and you have a visa, you can enter the US to work for employer A. Before making travel plans you should confer with the...