Regarding (A) - I have MobileChat installed and it is designed to do the exact same thing - it runs in the background, maintains an open AIM connection, and displays an SMS-style notification if you get an instant message. So... obviously if they are keeping a client socket open, we must be able to do that too. Also, I've managed to SSH into my phone when the screen is off and the phone is locked. I'm not sure if there's a deeper mode of "standby" than that.

Regarding (B), Mail.app always does a poll when you open it, right? Forcing a background Mail.app poll, well I don't know how we'd do that, and it seems like we'd just be doing double the work that way since it will inevitably poll when the person clicks on the icon a second later.

Playing a sound or vibrating is just a single API call, and seems easier to me. Actually, you can play a sound from the command prompt with the "playaudio" command, I believe. Dunno how to update the mail icon image in the dock, but it can't be that hard.