Throbbing vein (with pulse) appears on forehead after exercise, if I bend down and if I smile. Can it be removed safely? (Photo)

I use a combination of treatments simultaneously and inject with sclerotherapy to obliterate small branches and make the vein smaller by spasm and use this as a tool to enable tiny micropuncture wounds to remove the vein via  technique called sclerotherapy. Such incisions can heal quite nicely with little residual. Expect to pay approximately 2000 dollars. 

The forehead vein that you show actually is a quite common complaint for facial veins.  It appears to be relatively large. The best treatment for this would be removal through 2 or 3  small incisions (microphlebectomies).  The trade off is that there will be 2 very small scars. The alternative to this would be sclerotherapy but this is actually more difficult to do and requires multiple treatments. Another option would be to just leave it alone.