I have a unilateral pulsatile tinnitus. Is it serious?

Possibly serious. Most likely a serous otitis (fluid in the middle ear) placing pressure on the inner ear. However, more serious but rare cause could be a carotid or other artery aneurysm, therefore this symptom should be evaluated by a your physician or an ENT md.
Possibly! Pulsatile tinnitus, particularly if you hear your heartbeat, is usually nothing to worry about... But my job as a physician is to worry for my patients! the concern would be (especially in older patients or those with risk factors for stroke) narrowing of blood vessels in the head and neck, creating turbulent blood flow - and therefore pulsatile tinnitus. Worth getting checked out.
Unlikely. Pulsitile tinnitus is unlikely to be serious. It may be caused by the blood vessels and carotid artery which runs right next to the inner ear. It could be high blood pressure or stress. There are some benign tumors that can cause it as well. You should see your local ent.