Should I breastfeed if I have a fever?

Yes. In general, the most common cause of a fever in the mother is a viral syndrome such as a cold/flu. A breastfeeding mom should not stop breastfeeding just because she has a fever. The antibodies that she is creating to fight her own infection are pasedt through to her baby via the breastmilk. So, she is in fact also providing protection from infection while continuing to breastfeed.
Yes. Yes. If you have a fever, drink extra fluids and continue to nurse-- if you get engorged and uncomfortable, you'll only feel worse.