Fever can support the immune system's attempt to gain advantage over infectious agents, such as viruses and bacteria, and it makes the body less favorable as a host for replicating viruses and bacteria, which are temperature sensitive. Infectious agents are not the only causes of fever, however.
Your sister's grandson is your great nephew. You are his great aunt (if you are a woman) or his great uncle (if you are a man).
Your brother's 12-year old daughter lived with you for 7 months out of the year. You, your brother, and your father each provided some of her financial support during the year--but she provided none of her own support. Your niece meets the requirements to be your Qualifying Child, and you can claim her as a dependent.