Do you have to stay away from sick people with leukemia?

Depends. It depends on the leukemia, treatment, and other factors. Some leukemias may not be treated (cll rai 0) or due very well as a "chronic disease" (cml treated with gleevec). Other leukemias may increase risk of infection (eg, cll with low immunoglobulins; AML on chemotherapy, etc). Standard precautions to avoid obviously sick people are reasonable. How vigilant to avoid people depends on above.
It depends. People with leukemia many times have decreased immunity so if you are sick you should probably stay away so you don't make them sick. If they already have a bug you may catch it like you could from any other sick person, not only people with leukemia. Generally speaking, the risk is higher for them to catch a bug from you than you from them.