None. Hinduism and Buddhism share no sacred texts.
Hinduism believes in a Creator God, while Buddhists do not. the case system
Both believe in it.
No, Hinduism and Buddhism are two separate religions, even though they share many beliefs about compassion, kindness and charity. As it was Hinduism was in its infancy when Buddhism started. Ancient Hinduism was more closer to Brahmanism than the Hinduism that exists today.
They both believe in reincarnation.
The main one is the belief in re-incarnation.
they both originated in the sub content of India
There were several concepts that are not shared by Hinduism and Buddhism. One of the most prominent is atma. According to Hinduism, all beings have an unchangeable, eternal self or soul. The Buddha instead taught anatta, that there is no self at all, that the self is an illusion.
Buddhism is a part of Hinduism in the sense that Christianity is a part of Judaism. "Buddha", or, Prince Siddhartha Gauthama was of the Sakya clan, a Hindu clan in present day Nepal. He was raised an orthodox Hindu and eventually went off to pursue enlightenment which was not an unusual option of that era for a man of his station and religion. One of the problems that Buddha had with Hinduism was the caste system and later when he was teaching he stressed the equality of human beings from a spiritual or karmic perspective. Buddha was a Hindu reformer and taught essentially Hindu teachings and practices. Much of what is called Buddhist practice is common to Hinduism. In this way Hinduism and Buddhism are related in much the same way that Judaism and Christianity are related, Christ being a Jew reformer. But no, to specifically answer the question: Buddhism is not formally a "part" of Hinduism. Then again, there is no such thing as "Buddhism" outside of the west any more than there is a such thing as Christism. In "Buddhist" countries the practice is referred to as "Dharma".
Hinduism and Buddhism share many common effects on each other. Like Austerity (tapaḥ) Purity (shaucham) and Compassion (dayā) being part of both religions.
Buddhism and Jainism share similar beliefs in non-violence, karma, and the pursuit of spiritual liberation. Both religions emphasize the importance of leading a virtuous and ethical life, and both reject the caste system and ritualistic practices. Additionally, both Buddhism and Jainism advocate for the practice of meditation as a means to attain enlightenment.
Your question does not make sense since there is no such thing as Hindu Buddhism. Hinduism and Buddhism are two distinctly different religions. Though both religions share a common belief concerning personnel growth to attain enlightenment, Buddhism does not concern itself with Gods or Deities, nor does it have set rituals. Hinduism, on the other hand, does have both.