Can my husband be deported because he got a second dui?

Yes, that's a distinctive possibility if ICE learns of your husband's being held in jail and seeks to "secure him" after release from state custody.

I came USA from Nepal in f1 status, but now it's been 3 years since i've been out of status. I have TPS and advance parole.

There is no way to reinstate that F-1 status when have been out of status for already 3 years.

What if I end up overstaying my I-94 return date while waiting for my advance parole and then travel out of country?

Even though could be readmitted based on AP, USCIS is a master in concocting "inadmissibility grounds" during the interview based on your travel on...

I have lost I-797 what should I have to do?

Best to try to sort this out during an INFOPASS appointment at your local CIS office.

I751 immigration case?

Stranger things have happened before. Worry not. Remain patient and schedule an INFOPASS appointment at your local office.

How long does it take normally for replacing a stolen green card ?is there a way to expedite the process?

Nowadays takes a very long time for USCIS to process an I-90 application. Sometimes even 9 months or so. Cannot be expedited.

What should I fill in I-765 section 15 for c3b (F1 visa) while I just submitted and only got the receipt for another I-765: c9

I agree with Mr. Behar's excellent answer & explanation.

How long a person need to stay with Company after getting GC?

Long enough to convince CIS during your citizenship interview that you have not in fact committed immigration fraud by later resigning from that...

How should I convince visa officer that old and new company are same during visa stamping?

Not the type of questions to be posed on a general, free blog on the internet.

An EAD application cannot be normally expedited and certainly not under the facts you are mentioning here.