About 5000 miles or more or less
Buddhism
The farthest west reported is till Herat, Afghanistan. In east, it reached Japan.
It first spread to China and Sri Lanka. From China it spread to Tibet, Japan and Korea. From Sri Lanka it spread to the rest of South East Asia.
Yes. It's a South Asian belief which origionates in India and later spread across South East, and East Asia.
Buddhism and Hinduism were introduced to South Asia by India. Buddhism has gradually declined in India, but it is still very strong in South Asia.
Hinduism made an impact because it gave birth to other religions such as Jainism, Buddhism and Sikhism. Hinduism also had an impact on economy by the entire community learning to be self-reliant.
Asoka, the emperor of India, was the cause; because he was a faithful Buddhist, so he tried to spread the Buddhism to the world, and he did. By using his empire's influence, Buddhism was spread to Southern Asia and today's middle east; few hundred years after he died, Buddhism was introduced to China in Eastern Han dynasty
because Buddhism is mostly implemented in places like Nepal and Burma as the major religion of India has and will always be Hinduism
Cultural difussion
Buddhism started in Northern India in about 2500BC. I first spread in India and then China. Since the Buddha's death it has spread throughout most of east Asia, Europe and now the America's. Buddhism is the 4th largest religion in the world.
The farthest west reported is till Herat, Afghanistan. In east, it reached Japan.
Tofu most likely originated in China, in the second century BC. Its spread into other parts of East Asia may have coincided with the spread of Buddhism, because Buddhists are vegetarians.