Yes, they can. Anyone can adopt a child if they have no place to live and are currently enrolled in a school. Is the child a US citizen? If not,regular INS procedures will have to be followed to establish his residency status. Simply because he is a child does not guarantee he will be allowed to stay in the US even though he has a relative who is a citizen. If he is a citizen the aunt can initiate adoption procedures with the permission of the mother. It would be best to consult an attorney who specializes in Immigration law.
Yes, if all parties are in agreement.
This depends on the legalities of the area you live in as well as the wishes of the mother/family.
You can adopt someone to be your child but to be your nephew he had to be adopted by your siblings. Then he will be your nephew. There is no nephew-adoption.
You're a Great Aunt to your nephew's son, who is your great nephew.
a nephew's kid to his aunt's kids would be their cousin.
You are your nephew's uncle, or aunt, and his son's great uncle, or great aunt. Your nephew's son is your great nephew.
Your niece's son is your great nephew. You are his great aunt or great uncle.
Your nephew's child is your great nephew (if a boy) or great niece (if a girl). You are his or her great aunt.
You are a great great Aunt (or Uncle) to the grandson of your Nephew.
Your brother's (or your sister's) son is your nephew and you are his aunt if you are a female or his uncle if you are a male.
Aunt.
To your uncle, you are his niece or nephew.
You would be his great aunt. To you he would be your great nephew.