Yes, but it could be quite a challenge. The court would look first to the biological parents then grandparents, and other close relatives. If the court checked your background and found you to be the best fit for the child , yes you could obtain guardianship.
You are an aunt/uncle-in-law! Congratulations!! You really are; because you're an aunt/uncle to your niece you are now an aunt/niece by marriage to her husband.
Your niece in-law, or your niece by marriage.
Your niece will call you her aunt or uncle.
uncle, niece
Your niece's children are your great nieces and great nephews, and you are their great uncle. Your uncle could be the father of your niece, and thus the grandfather of your niece's children.
A niece's son calls his uncle his uncle, just like everyone else.The niece's son calls her uncle his great uncle. He is the great uncle's great nephew.
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
There is no legal relationship, but most people would refer to him as their nephew. I typically introduce someone like that as the husband of my neice. Going the other way, I usually refer to them as my wife's Aunt or Uncle.
You are her great-aunt/uncle. She is your great-niece.
Your brother in law's daughter is not a blood relative; however, by marraige she is your niece. She is the neice of your wife. Any relative of your wife becomes a relative of yours when you become "one" in marriage.
Not if they have guardianship.
You are your uncle's niece. You and your uncle's children are first cousins to each other.