Anemia and rhythm. Anemia can be checked for with a complete blood count. While either anemia or heart problems can be hereditary, they don't usually occur together except in conditions like thalassemia or diamond-blackfan anemia. Theoretically, problems with the band 4.1 protein in red cell membranes could cause anemia and slow heart rates, but this hasn't really been reported in humans.
Yes, but... There is no inhereted condition that causes both anemia and arrhythmia at the same time that i know of. There are many inhereted causes of anemia, such as sickle cell and thalassemia and these are quite common. Even so, most anemias are not inhereted. There are inhereted conditions that cause arrhythmia, but they are uncommon. A physician should be able to tell you if a condition is inhereted.