What is the ruling on the Umrah of someone who left the tawaf without knowing how many circuits he had completed, then returned to complete it, then trimmed only a few hairs from his head, then repeated the entire rituals again and shaved his entire head?

If you doubt the number of circuits (ashwat) of tawaf, you should base it on the certain (lower) number and then complete the rest. However, if the doubt occurs after finishing the tawaf, it is not given any attention. Since you exited and then returned to complete the tawaf, your tawaf is valid, as continuity (muwalat) in tawaf is considered a sunnah by many scholars, and a slight interruption is not considered to invalidate it. As for what you did by cutting some hair, it is not sufficient for disengagement (tahallul) according to those who deem it necessary to shorten or shave all head hair. However, since you have re-shortened all of your head hair, your 'umrah is complete. Regarding the prohibitions, those that are for indulgence (taraffuh) have no penalty. Those that involve damage (itlaf), such as shaving hair and cutting nails, require one fidyah for each category. The Shafi'is hold that shortening three hairs is sufficient for tahallul. According to this view, taking those hairs is sufficient for you if they were three or more, and you would be disengaged from your 'umrah if you had performed tawaf and sa'y, and nothing would be required of you.