We just noticed fleas in our home today, from previous person that lived here. Exterminator comes in a couple days. But I have a almost week old baby. Can the fleas hurt him!?

Yes. Flea bites on humans can transmit various types of disease. Usually, they result in just plain itchiness which can drive one nutty - imagine a poor baby. However, the itching and scratching can result in superimposed infections. Another concern is that most products used by exterminators (e.g. Fumigation) can be very harmful to humans - please ask what chemicals they will be using.
Probably not. Fleas will bite anything they can reach and keeping the baby away from the floor should help prevent bites until the house is treated.