hahah yes, you got it!
Wow, it's surprising to find out such things. And kinda disappointing too, because most Hindus when they see others practicing or following their traditions or having Hindu icons, think that they're revered by others as much as they're revered by Hindus themselves. But then, like recently Harrod's of London was selling Hindu-themed bikinis with Goddess images on them, it's not always the case.
Yes, jax, yoga is a Hindu tradition. "Yoga" means "joining with God" because Hindus believe that our souls never die even when we do, that the soul is the essence of humans, and that through meditation (yoga is supposed to help one in one's quest for perfect meditation) and righteous living (called "dharma"), one can get one's soul to rise to higher states of consciousness until at last it unites with God, or the Super-Soul.
But of course nowa-days, yoga is used by most folks as simply exercise and nothing much else. I'm glad though that your yoga instructor does relate it to Hinduism in his/her own ways.
And yep, Hindus believe in reincarnation, in that this physical body is just one "home" of your soul, it is the soul that moves on when your physical body passes away, and the soul reincarnates according to its "karma".
And yes, Hindus believe in chakras (part of "kundalini"). Kundalini chakra is the highest chakra of the seven that run up one's spine. When one achieves the higher states of consciousness through yoga and meditation, one is able to arouse the Kundalini Chakra and then one can feel the nature of this Creation and become Self-realized. Jesus too is supposed to have said the same thing, in a different way.
And yes, Ganesh (also written as Ganesha, with the last 'a' silent) is the god of wisdom, remover of obstacles. Students pray to Ganesh most often. :-)
Sharing this information is so exciting!! :-)
[q]It is through the sanction of the Gods that the Hindu undertakes the practice of yoga - that orthodox and strictly Hindu science of meditation that leads to union of the many with the One. Yoga is the culmination of years of religious and devotional service and can only be successful with the support of the Gods who are the sentries guarding the gates of the various strata of consciousness. This sanction, once obtained, can and does allow the kundalini force within the core of the spine to safely rise and merge with the Supreme that all Hindus know is the Absolute - timeless, causeless, and spaceless. But first much work has to be done, much work and worship.[/q]
http://www.himalayanacademy.com/books/pamphlets/GodAndGodsOfHinduism.html