I would like to be able to view DVD movies stored on a USB hard drive using the Roku 1000. What is the minimum network speed required?
The very minimum? 10 Mbit/s for DVD. The maximum stream rate for DVD is a bit below this but you'll want to allow for a bit of extra space.
100 Mbit/s wired would be best.
Remember that the quoted speeds for wireless are not realistic in real life, so for example theres no way that an 11b wireless would properly handle DVD streams.
Can I connect the USB 2.0 hard drive directly to the Roku?
No. It doesn't have the ability to use hard drives directly connected via USB.
Will the following connection scheme work? USB 2.0 hard drive -> network adaptor (eg. D-link DNS-120) -> Linksys router -> Roku 1000 via ethernet cable. No wireless here.
If it supports SMB (Windows Sharing), which I think it does, then the above looks fine.
If I want to go wireless will the new "pre 801.11n" routers work?
For DVD it should be able to handle it.
Remember if you decide you want to watch HD stuff, all your speed, network requirements etc. will greatly increase (though wired 100MBit/s would still work fine).