Hi @chazapanta
Yes, some of the mountain in Tibet are part of the Himalayas. There are thousands of attractive mountain peaks in both Nepal & Tibet. You can start with small mountain peaks at first. You can contact some trekking agents in Nepal, if you are really interested.
Yeah I agree to start with the small peaks of Himalayas as a beginner. Great! I'll google some agencies for my trek. How about the monks in Tibet? Is there a place to sleep overnight and get to know them and their culture?