Divx do have an .avi extention.
Rename is not necessary. If your dvd player doesn't play divx file, then you need to transcode to the format that the dvd player that will play it. Is that what you have in mind?
My suggest is just to buy a player that supports divx (they are not that expensive).
In general, video file can be put on a cd, but we want to know what video format you want to put on it first then I can comment on it.