Is it serious to have a heart palpitation and a murmur?

Usually not: Generally the two are not related to each other. A murmur is a sound caused by the flow of blood in the heart. In children and young adults, most murmurs are normal sounds ("innocent" murmurs), but some may be caused by problems with the heart. Similarly, most palpitations (feeling the heart beating) are also normal, but they can also be caused by abnormal heart rhythms. Check with your doctor.

Depends: Depends on what your actual symptoms are and the severity. I would recommend that you be evaluated by your physician to determine if you need an echocardiogram to further evaluate.