Despite the poor organization of my two previous posts, I hope to rectify that here.
How exactly does a GM or PC use any of this?
Well. Let's break it down.
Purusharthas (human purpose)
I've said this before. It makes no sense to me that only priests are religious in D&D. Lame. Just lame. That said, dharma, kharma, moksha, and samsāra should be important to all PCs.
The ātman should also be important, as all people are therefore divine and concerned about the afterlife. GMs pursuing a campaign world based on Hinduism need to work out some of these particulars with the PCs beforehand. Make sure they understand the importance of faith.
Vedic teachings vs. Non-Vedic teachings
Does the GM want peace between the two schools of thought? Open war? With so many interpretations, even on the Vedic side of the equation, how can one religion ever be consistent. This is ideal story-fodder for a gaming environment. And if PCs want to write up some Vedic scriptures, let them go nuts.
Principles and Commandments
Excellent debate material. And a great foundation to aid roleplayers. Remember, priests aren't just healing batteries.
The World is an Illusion
GMs and PCs looking to explore the space beyond the ephemeral, have all the tools they need now. Anything can be explained. Even magic. This also gives strength to zealot priests who preach of less permanence in the world around them (druids).
Western gamers are sure to hate this. Which is hilarious, because what is a class-based gaming system, but just another caste system. Nope. Only wizards can do that. Why not make the PCs work in a specific caste? Could it really hurt for one campaign?
Hindu notions of evil conflict greatly with "alignment" systems, which can be a good or bad thing, depending on your point of view. I really can't address this one for you. Sorry.
Hinduism is so diverse, it defies easy categorization.
Hinduism has no real begining.
Could a GM ask for anything more?
God (lower and upper case)