I don't know exactly what would be a normal rate, but if your baby's heart rate is ever approaching 200 beats per minute or too fast to count, you should definitly have him/her seen by a pediatrician. Infants can have supraventricular tachycardia - which can be serious if left untreated. Fortunately, the condition is totally reversible with adequate medical care.
I can't help you with that one. I have no experience with infants.
Probably best to ask a pediatrician.
I googled and it said anywhere from 110-160 bpm.