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).
If your child and your sister's grandchild are the same age, they are still considered to be one generation apart. For your second example, I assume that when you say my cousin, you mean your first cousin, i.e. one of your parents and one of their parents are siblings. Let's look at the generations.