The Buddha, originally Siddhartha Gautama, was born in what is today Northeastern India. He was born a prince and what he was exposed to on the streets caused him to see death, injury, depression, and poor people. He was later enlightened under the Bodhi Tree, becoming the Buddha.
Yes, The Supreme Buddha can be born out of Tibet. Where a Buddha is born is depends on the karma of a country. When China's PLA took over Tibet, Tibet no longer was a Buddhist haven. As of now India is where most Tibetan lamas reside.
Yes, I do believe in Buddha, because Buddha Ji was born in my Country Nepal. It is very easy to believe in actual historic figures like Buddha, Richard the Lion Heart, Mao Zedong, and Alexander the Great as they have a wealth of contemporary information as proof of their existence.
He was born around 2500 BC. As I am a strict follower of Buddhism I know the whole Biography of lord Buddha, that i can surely conclude that Buddha was born in Kapilvastu (district), Lumbini (zone), Nepal.