I think you won't regret buying the SL-C1000.
VGA Display, very good battery life (1800mAh), USB host and client, 128Mb flash.
It's relatively cheap compared to the 3100, so that there is large user base. A couple of developpers bought it too. For example, Mavlovsky who will soon release the new Cacko ROM(a matter of weeks), CoreDump who released the Hentges ROM (a well tuned OZ-Opie ROM especially for the C1000), the PdaXrom team have a few C1000 also.
1. How good is battery life with the C1000? I did buy the (older) Socket CF wireless lan card to help with battery life.
Very good battery life and your WiFi is well supported in all ROM
2. What ROMs are available now that work well and are stable on the C1000?
OZ-Opie, PdaXrom, very soon CackoROM, and obviously SharpROM
3. The software I'd like to run on the C1000 would be something like: a ICQ client and NES emulator (among other small utilities and whatnot). Do decent GUI-based ICQ clients and NES emulators exist for the C1000?
I've tried NES emulator on a SL-6000L, it was working great, never tried on the C1000 but I don't see any problem why it shouldn't.
There are instant messaging software working for each ROM: from memory gaim(quoted from the cacko feed for C7xx: A multi-protocol instant messenger client,
supporting AIM, ICQ, MSN, Yahoo!, Jabber, IRC, Zephyr,
Gadu-Gadu, Napster, and Trepia) is available for SharpROM and HentgesROM, xchat is available for PdaXrom, and probably other packages like irc, qazoo, ...