Such a child might or might not have birth defects. That depends on whether there were tendencies toward such in the family, and how strong the genetic signal might be. Even if there were tendencies, there is not certainty that a defect would show in any specific child of such an incestuous relationship.
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.
You are her great-aunt/uncle. She is your great-niece.
You are the great-great-aunt/uncle to your niece's granddaughter. This means that your niece's granddaughter is your great-great-niece. The term "great-great" signifies that there are two generations between you and your niece's granddaughter.
You are your uncle's niece. You and your uncle's children are first cousins to each other.
great niece
'Niece' is what a little girl is to her uncle. 'Nephew' is what a little boy is to his uncle. The children also are the niece and the nephew of their aunt.
Uncle
Your niece in-law, or your niece by marriage.
To your sister's daughter you are an aunt (or uncle) and she is your niece. To your niece's daughter ( your sister's granddaughter) you are a great-aunt (or great-uncle) and she is your grand-niece.