If you 'feel' your heart, is it a sign of heart issue?

Not necessarily. If one notices their heart beating, it may be due to exertions, excitation or anxiety or stress. If this is causing you distress, yoiu may need to have it checked out. You could have a thyroid condition, other metabolic condition or just be out of shape. If there is shortness or breath, chest pain, dizziness, decreasing endurance or other issues, see your pcp and discuss.
Possibly. Some patients with high blood pressure - report hearing their heart beat in their ears or feel their heart beating harder in their chest... So the first thing i would advise is get your blood pressure checked... And see your md to actually take your BP and listen to your heart and maybe even have an EKG to look at the electrical activity of your heart.. Best to you!, hope that helps!