I can only address your questions about Blackdown, as I was able to install it and run on my Ipaq 3670 with familiar 0.7.1 (see comments on http://www.handhelds.org/z/wiki/BlackDownJavaOnFam07).
1. It depends on what you need it for. Although Blackdown is not very fast, well written java program should be fine. I did real time graphics display with AWT and had no problems. And I used ipaq 3670, that is slower then 3970.
3. If you install familiar with Opie, then AFAIK you should be able to run everything like on Zaurus.
4. Networking is not a problem, I run java communication via wireless network.
5. There is a Swing example that comes with Blackdown.