You must to make your Wii to be modified with a mod-chip before you play games or movies.
Of course it can play any game of your own, and any movie (also DivX as you asked) as you wish after you get your wii mod-chip installed!

It's a very mature technical now so it won't have problem if you get your wii modified.

Also you can download any PAL or NTSC Wii game as you wish online now.

About the downloading and backup and copy games service: There are serveral sites providing such download services. They are very excellent on the contents, not only Complete big Wii games like Metroid, LOR, American Idols and Guitar Heroes etc. But also many movies, Wii tv shows, music and videos much more!!!

All you need is to join one of those sites to download so many resources. So you can download all those media as you wish!

And some sites can provide simple software help you to burn the ISO Games into DVDs, it is very easy and fast. After the instructions by them, you can go ahead to play those games you burned onto your Wii.

Good luck and have fun with your Wii!