Hinduism is never taught, It is experienced & followed in the countries of Nepal, India & Berma.
Buddhism taught Hinduism Non Violence & Peace. Islam taught to accept different belief & rituals, also some of the rituals were affected.
Teachings of Lord Brahma or brahman is the base of Hinduism. Lord brahma taught first man Philosophy of life and way of living, it is now known as Hinduism.
Islam.
Hinduism teaches Kāma (enjoyment) Moksha (liberation) Artha (material prosperity) AND Nirvana (Liberation) . Also Hinduism teaches Reincarnation (punarjanma) AND Incarnation (avatāra) laws. And The Law of Cause and Effect (karma) . Peace and Non Violence is also taught by Hinduism
In south east asia Hinduism not only taught people way of life but also some important way of earning money as well. This made followers of Hinduism rich and wealthy.
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.
Yes Hindus were there in India when Jesus was born, as we must remember that Thomas came to India and converted the Hindus there.
Hinduism did not influence Indian society and culture, Hinduism was Indian society and culture. One could more ask how Judaism influenced Israeli society and culture. It is not a system of beliefs superimposed on a way of life but it it a way of life expressing itself as a system of beliefs. Several systems of belief, honestly, all encompassed within what is known to the rest of the world as Hinduism.
The biggest influence of Aryans to India is Hinduism, a religion that majority of the population still practice up to present. They also influenced India to use iron tools. They taught Indians how to make weapons.
Hinduism and buddism
Hinduism