If i was granted deferred action but i would like to use my husband last name what can i do to change it?

You can file for a replacement employment authorization document.

How long it will take CR1 visa

It takes about a year.

Is SSN number mandatory to apply for EAD under L2 VISA

It is not required, on the contrary, you need an EAD to get a SSN.

I've already had B1/B2 visa for tourism. Do I need to reapply B1 visa for independent research in US?

You do not need a different visa, if you are keeping the terms of your B1/B2.

I was granted DACA and I also have a I-130 approved I would to adjust my status here, should I apply for an advance parole?

Yes, you should apply for advance parole.

Can I travel before H1b approved?

It should have no impact on whether the visa is approved or denied. It can affect whether you are granted a change or extension of status.

Can I Work for my employer outside the US for the total time of the greencard process, and maintain a legible LPR application?

You do not need to work with the PERM petitioner at all, in or out of the U.S., until and unless the visa is approved and issued to you.

Is immigrant visa the best one for me?

Your best chance of being approved is an immigrant visa together with a K3. That lets you travel to and from the U.S.

Regarding your first question, I wonder why you would want to withdraw your request, since it could leave you without status? There is no set...

Oath que

There are great differences depending on the nearest federal court and the court's schedule.