The dentist may use anesthetic such as 0.3ml lidocaine with 1:100, 000 epinephrine. Would this interact/ have problems with my heart or BP medication.

Little concern. Stress form the procedure, particularly if you were not numb, would cause your body to release more Epinephrine then what is in the local anesthetic. That said I do try to error on the side of caution depending on the heart condition by not using the maximum dose( approximately 8 full injections) and breaking up multiple procedures over several appointments.
Probably not. 0.3 ml is a small dosage and 1:100, 000 Epinephrine is also a lower concentration. There are dental anesthetic agents that have 1:200, 000 Epinephrine as well as anesthetics that contain no vasoconstrictor-which i often use for smaller or faster dental procedures.
No. It is unlikely for Epinephrine to have any interaction with your BP medication but you may have the following: Epinephrine keeps local anesthetic at the site, making it work more profoundly and for a longer time. If some of the Epinephrine is absorbed directly into the bloodstream or if you are particularly sensitive, the side effects may manifest as a racing heart, palpitations, or dizziness.
Very unlikely. Although your dentist should be aware of the situation. The Epinephrine is used to constrict blood vessels an keep the Lidocaine in place. Therefore neither gets into your systemic circulation in any significant amounts.