If I'm male, then how do my sister's son and daughter relate to me? If I'm male, then how do my brother's son and daughter relate to me?

Family relationship terms can be tricky, especially once you get into first and second cousins twice removed. See the link below for a handy chart for figuring out those terms. 

If you're male and your sister has both a son and a daughter, then her daughter will be your niece. Her son will be your nephew. You will be their uncle. If your brother also has a son and a daughter, then his son will be your nephew and his daughter will be your niece. You will be their uncle. Your sister will be an aunt to your brother's children and your brother will be an uncle to your sister's children. Your brother's children and your sister's children will all be each other's cousins.