If Eclipse hangs while “building workspace”, try killing any running adb processes in the background. There actually seem to be a variety of possible causes, but when using the ADT Eclipse plugins, this might work.
Android Market Downloads not starting seems like a common issue. I used to have this problem a lot, and most of the time, rebooting the device would fix it. But, a couple days ago, even that stopped helping. After lots of random experimenting, I can happily report that I think I found what 95% of the time caused the issue (in my case anyway, YMMV): It turns out I had disabled the Google Talk Boot Receiver using Autostarts, ironically my own app. For some strange reason, this seems to prevent the Market from downloading. It might then also explain why rebooting used to help – I probably just used to occasionally shutdown the Google Talk service (shoutout to Advanced Task Manager), which then started all the trouble.