Does anybody know if you can open a movie (.avi) file with blender and render it with blender, or does it have to be done frame by frame?e

It’s not very clear what you mean. Do you want to, for example, have a TV set playing a movie in your animation? Or do you want to composite stuff you animate in front of an existing animation?

For the latter, use the sequence editor to compose video and render to AVI or MOV.

For the former, UV map (or any other form of texture mapping) your picture to a plane (or whatever the object is). Once you’ve got it mapped using the Material buttons (F5) and the Texture Buttons (F6), use the far-right panel in the Texture Buttons (‘Anim and Movie’) to control what parts of the movie appear over specific frames of your animation.

Hope this helps.