Do I need tripods etc. for filming?
A fig rig would be an excellent choice for an action piece. If the fig is out of your budget range look at the Opteka X-Grip. Cheap ($30) and pretty flexible, especially if you mount it sideways instead of with the handle parallel to the lens barrel when the shot needs it.

Also if you have access to After Effects spend some time learning the stabilization and tracking capabilities. That will probably improve your shots, helps with rolling shutter issues too that you may experience on a DSLR.

Borrow a tripod. Lots of tripods sitting around in closets in this world.

Edit: Audio is the achilles heal of DSLR video. Make sure you take that into consideration. You can pick up some decent but cheap shotgun microphones that will plug into the D7000, that will help. Also consider grabbing an H4, or several H1s.