Question unclear. The temporal lobe is part of the brain. How are you aware of a throbbing vein in that area? If you have neurologic symptoms, probably need to discuss with your doctor or neurologist.
May be normal. In the front part of the temple is the temporal artery which has anterior, and posterior branches. What you are feeling may be normal. The concern is if this vessel is tender, an indication of giant cell arteritis which can lead to blindness if not diagnosed. If so then have it checked.
Depends. Have a headache? Is it the first time? Visual disturbance? Red eye? Nausea? Light sensitivity? If you answer yes to any of these questions or still have questions see your doctor.