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.

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.

NEOCam wouldn't need cryogen, and it would also be able to see entirely new areas of space. It can scan the sky in a new way.