I think you meant to say Move as fast as you Think - many people have instances where they think far faster than they move.
On the Kakama Nuva being faster than the Kakama - no. It was never displayed as being faster, but it did something much more valuable than that, allowing the user to share that power with everyone around.
That's correct, it doesn't. But it brings up another point - it's that the Kakama lets the user do certain things, but the Kakama Nuva would let them do it better. (i.e. disrupt the form of antidermis on the molecular level, etc.)