Yes, you can play and store divx movies on a modded xbox.

You can play game backups, but not online - xbox live will permanantly ban you if you play online with an mod chip.

Once modded you can upgrade the harddisc. You can upgrade the memory on hardwarea versions prior to 1.6 by soldering memory chips onto the motherboard. Linux (afaik) & the dev kit make use of the extra memory.