Assuming there was no will which specified the bequests, it would depend on state intestacy laws.
If your brother (or your sister) has children they are your nephews (males) and nieces (females).
The living sister would be qualified as long as she is not under 19 years old.
If it's your sister then your sister, if it's your brother's wife then you sister-in-law
Jeremy Wade is the unmarried Uncle of many nephews and a niece. He has a brother who is a teacher and a sister as far as I know. His parents are deceased. No wife yet
Your sister-in-law is either the wife of your brother or the sister of your spouse. The children of your brother's wife are your nieces and nephews, since they are also the children of your brother. In some cases they may be your sister-in-law's children from a previous marriage. Then they are not related to you at all. However, if they are very young, it may be convenient to call them your nieces and nephews anyway. The children of your spouse's sister are always your nieces and nephews.
Your sister's husband is your brother-in-law. Your brother-in-law's brother is not related to you and neither are his children. But he is your sister's brother-in-law and his children are your sister's nieces and nephews.
Nephews are the sons of your brother or sister. Therefore nephews who are not brothers to each other are first cousins to each other.
Niece is to nephew as sister is to brother.
The children born to your siblings are your nieces and nephews.
It will be split in half, half going to brother, half going to the issue of the sister.
Yes
The nephews and nieces have equal standing under the law. However, if one wishes to speak of royal precedent, then the deceased's eldest sister's eldest son, and if she had no son, then the eldest son of the oldest sister who did have sons.