Filing does not void the C1/D1. If is possible your fiance may continue using the C1/D1 if your fiance is able to convince CBP that he he will...

Domicile

Your domicile is generally considered to be your principal place of abode or your residence.

AOS Interview

Generally for adjustment it is not requested.

Can I change my Employer?

It is possible. Speak with your employer's immigration attorney.

I am planning to split my name on Indian passport.is it necessary to change name on i-797?

You will need to change your name at time of extension or other application, not on an already filed and approved petition.

Change H1B employer before October 1st

You may have more than one approved H-1B for different employers. Talk with your employer's immigration attorney to determine if this is feasible...

DS160 form - "Has anyone ever filed an immigrant petition on your behalf with the United"

Yes since a petition was filed. If there was never a petition for the other family members the answer is no

Filing for H1-B transfer and H1-B to H4 at the same time

Better option is to depart the US obtain the H-4 and return to the US

Change of status from H1-B to H4 and file H1-B transfer between employers at the same time

You will not be permitted to withdraw the H-4 and file H-1B you will need to either have the H-4 approved or recommend depart the US and obtain H-4...

Can I extend visitor visa for next 5 months for my cousin as she is pregnant?

Pregnancy is Not a valid reason to extend.