iCam currently doesn't display badges. Badges will be added in an upcoming iCam update.
I don't know too much about routers. I have an Apple Airport Extreme that has worked well for me. Before that I had a Linksys WRT54G that also worked well.
If you're having a problem with the dynamic IP changing too often on the camera, you can set the Linksys WVC54GCA to use a fixed IP address in the camera settings, under Basic settings.