NASA has hit a comet with an impactor, during the Deep Impact mission. The goal of that mission was to study the surface by making a crater and stirring up the surface material so it could be studied.

I think Dawn has done an amazing job showing that asteroids aren't just hunks of rock. They're worlds - they're places an astronaut can explore. I think the Rosetta mission also did an amazing job of that.

NEOWISE has two goals: One is to characterize asteroids, figure out how big and how bright they are, really basic information about these bodies; and we also find asteroids.

Changing the asteroid's velocity changes the time when the asteroid crosses Earth's orbit. After all, just because it crosses Earth's path doesn't mean there is necessarily going to be a collision. It has to cross Earth's path when the Earth is right there.