Are palpitations inherited?

Sometimes. Palpitations or the awareness of your heart beat is very common. It may be due to extra beats of the heart from stress, or med/diet issues. Others include atrial fibrillation which may often appear as you age. And, paroxysmal atrial tachycardia which may be inherited or be related to heart wiring issues at birth. Sudden cardiac death my occur in some families due to prolonged qt syndrome.
Not usually. Palpitations are due to arrhythmias and while most palpitations are due to premature contractions which are not inherited, there are some arrhythmias which are inherited, generally those that are more serious in nature.