Please help me to understand my next step for getting the SSN and EAD updated with after marriage name

Apply for name change with SSA and new EAD with name change.

Can i respond with affidavits? for a Notice of intent to Deny my green card?

Affidavits my be used but you facing a potentially serious matter and are better off seeking legal assistance then replying on your own.

Is it okay to use my husband's name in filling out the application forms without changing my name yet in my SSA and DMV card.

use your legal name. if your name was changed in marriage you shuld indicate the maiden name and any other names as well.

Can I answer with affidavits from my mother & my daughters mother and my affidavit.

Failure to disclose or concealment is may be construed as a misrepresentation. Work with an immigration attorney and this is a serious issue.

As my colleagues have noted employment on the EAD from asylum may violate the F status.

Can i answer with affidavits for a notice of intent to deny for a green card

Affidavits as part of a reply to an RFE are appropriate work with your attorney.

F1 Student + Asylum seeker work permit

As my colleague noted, working full time does end the student status. There are employment possibilities as an F but they are limited.

DUI "Administrative Processing" how long does it typically take for FBI clearance (i am currently in Mexico city) ?

Weeks to several months or more. There is no set time frame.

1. Will his visa change to H4 if my H1B visa is approved effective 1st of October?If yes, how do we revoke the H4 petition?

The H-4 needs to be applied if you are granted H-1B

What are the chances that her visa might be rejected as I am on H1b that allows to file for a Green Card?

Filing for resident Strauss for yourself should not affect J renewal for your spouse.