Can we (parents) get legal status to stay in USA based on my daughter medical condition(US born 5 months old)

Will be difficult, but not entirely impossible. Work with an experienced lawyer who will agree to take your case.

I am on O1A, My I-140 for GC under EB1 is approved,Does going through NVC reduce my chances for GC, I am from India?

I couldn't agree more. Avoid going to the consulate abroad for this.

How do I go about this?

I agree. You have to depart ASAP before you trigger the inadmissibility bars.

What are my options for a backdated H1B extension approval?

We know nothing about your case nor your employer. These sorts of questions have to be posed to your employer's immigration lawyer.

Why I didn’t receive any updates for my EAD,which I applied on dec 2018?

It's an odd situation. Should have received your case filing receipt already. Hopefully you paid with a check and can ascertain whether was...

Does h1b start date need to be on Oct 1 if previously held h1b subject to cap?

You are cap exempt and employer can request any start date he/she deems proper.

How does it work

Will be up to the CBP whether to admit you on your next visit or not, and especially on whether you accrued enough unlawful presence with which to...

What should I do if my EAD extension expired ?

If an employment based I-485, then need to stop working when EAD expires and will only be eligible to resume once new EAD in your possession.

How can I get visitor visa for my mother?

Unless mother can qualify on her own right, without necessitating any "sponsorship", affidavit of support and the like, here chances are slim, at...

Since yours is a civil and not criminal matter, should have no effect on your ability to either travel out or return to the country, unless a bench...