If I'm sick (aside from morning sickness) is this harmful to my unborn baby?

Depends. The answer depends on what you are sick with. If it's a viral infection, it may cause problems with the fetus. If it's diabetes, this can also impact the fetus health. I would consult your physician to consult with them about your condition.
Depends. Only germs that enter your blood, like flu or blood poisoning could get to baby and maybe cause a problem.Colds /sore throats/etc that stay local do not. As long as your health is good in general, baby draws nutrients from you in a protected environment.