Get married
Your aunt's daughter is your first cousin, as is your aunt's son.
Your niece will call you her aunt or uncle.
If your niece is happy about the baby, be happy too- say all of the things an aunt would say- "Congrats! Maybe it will be a Girl! Did you pick out any names yet? I am so happy for you!!!!" You could also offer to help out decorating the baby's room, or buying clothes and toys, especially if she has lost her primary source of income (Father) and in this economy. But DO NOT say anything about the father unless she really starts talking or venting about him.
That's easy cousins.
Your Aunt's niece is you (if you are female), your sister, or your First Cousin.
You are your niece's aunt, if you are a woman.Any of your sisters who are not your niece's mother are also her aunts.The sisters of your niece's parent who is not your sibling are also her aunts.
You are her great-aunt/uncle. She is your great-niece.
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 aunt's brother is either your father or your uncle. If you are a girl, you are always your aunt's niece.
Your aunt's son and her niece are first cousins to each other.
Your niece's son is your great nephew. You are his great aunt or great uncle.
The great aunt is the great niece's baby's great-great aunt.