I have some questions I hope some people can answer

I am helping my cousin find his brother that was given up for adoption at birth. I am wondering about some things and I thought I would ask here if anyone knew: 1. When a child is adopted they are given an amended birth certificate. Does this birth certificate get filed in the birth index with the regular birth certificates also? So if I was to open the birth index would I see the original birth cert and the amended birth cert on the same list? 2. Can a gay couple adopt a child? (I don't mean to be insensitive with this question but I need to know) 3. If a gay couple can adopt, how fast can it happen after birth? Actually for that matter how fast can anybody adopt after birth? (It may have been 2 men that adopted him, that's why I ask) 4. If a gay couple adopted him then how does one decide which name shows up as "mothers maiden name" on the birth certificate? Or is there a special birth certificate that shows 2 fathers names? I'm sure I will have more questions but this is what I can come up with right now. Thank you in advance to anyone that can help. I truly appreciate it.