Can a female with palpitations give birth?

Yes. Yes absolutely.. Cardiologists and electrophysiologists can take care of just about any heart rhythm problems to allow a safe childbirth. Be reassured and see your doctor.
Probably. Palpitaions are a symptom not a diagnosis. If the heart is structually normal on an echo and the lab values are all ok there should be no issue with getting pregnant and delivering normally.