Hi, I would recommend that you discuss this with your doctor.
Your Dr. would be able to say why that combination was prescribed, as it seems you have some fluid retention with your hypertension. …so with that combination, the pulse "volume" would fall but not the pulse rate. Lisinopril is a good ACE inhibitor which would do well with lowering your BP but the diuretic would help you to loose an extra amount of fluid via urine and hence lower your BP and sometimes pulse volume.
I hope this helps.

Unlikely. Neither of those meds should affect your pulse. Since you are having those symptoms, please see your doctor.