Since an iPod Touch can send iMessages, I would assume yes.
I would say you're correct ... I saw a post the other day where someone had deactivated their iPhone but was still receiving iMessages over wi-fi.
Yes. A short while back my iPod Touch took a dive and I replaced it with an iPhone (it was actually cheaper then the iPod Touch). I have used this for 6 months now and can do anything on the phone except make calls as there is no network behind it. I can sent texts over WiFi using an app, and all other functions do work including maps and GPS.