GC for Mother (Widow) - Marriage Certificate

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Hi Experts,

I am new to this forum hence apologize for any breach of protocol (if any) upfront.

Query is as Follows:
Applying GC for Mother (Indian Citizen, Widow) under Family based set up.
Applicant - My sister (US Citizen)

Concerns, Issues and approach we are following:

Marriage Certificate - We do need it?

Name Before and After Marriage - My mother took my fathers last name after marriage but we never legally changed it via a court order. Her passport and other identification documents have her last name after marriage

We do not have a birth certificate - We will procure Affidavits from my mother's relatives attesting to birth.

Fathers Death Certificate - this certificate does not have my mothers name on it but we have the original

Sisters Birth Certificate - we have this and it contains my mothers name

Any advice to the above is appreciated.

Thanks