Can she? Yes. Any female of reproductive age can make a child with any adult male who is able to perform sexually.
Should she? No. This is a close family relationship and sexual activity is sometimes considered to be incest
You are the great uncle of your niece's child if you are male. If you are female, you are the child's great aunt.
Great great aunt/uncle. To your niece, you are the aunt/uncle, to her child you would be the great aunt/uncle. So you would then be the great great aunt/uncle of her child's child (her grandson)
Your uncle is your child's great uncle. Your child is his great niece (if a girl) or great nephew (if a boy).
The child of your niece is your great nephew (if the child is a boy) or your great niece( if the child is a girl). You are the child's great aunt, because you are a woman. A man would be the child's great uncle.
you would be the child's great aunty or uncle Therefore, they would be your great niece or nephew.
Your sister's daughter is your niece. You are her aunt if you are female, or her uncle if you are male.
Your niece in-law, or your niece by marriage.
Your children are the cousins of your niece. Your niece's children would be second cousins to your children, and vice versa.
Your niece will call you her aunt or uncle.
A niece or nephew is the child of an aunt's or uncle's brother or sister. So the parents of the aunt/uncle and of the niece's/nephew's parents are the same people - their grandparents. The grandmother of the aunt or uncle is the great grandparent of the niece or nephew.
uncle, niece
Your niece's son is your grand-nephew. You are the child's grand aunt, or grand uncle (whichever applies).