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A lot of what you describe in #1 can be accomplished without an app, though I'm kind of confused by the description because right in the middle of listing features you just say "that can be downloaded from the app stores," which sounds circular: you need an app because you need something that can be downloaded from the app stores?
#2 is, if anything, easier without an app.
#3 is kind of a non-issue because there are lots of remotely hosted chat options. And I'm having trouble of conceiving of a site big enough to need an app, but not big enough to handle the fairly minimal server load involved with hosting its own chat.
Re: #4. I have no idea what "have my own app account system means." If you mean that you wanted people to sign up for new accounts with the app, separate from your existing user base, then that sounds like a very, very bad idea.
Overall, I'm fairly sure increasingly featured mobile sites are the future here, and not apps, but do what you wanna do. Unless you're actually trying to promote Chatwing, or whatever, in which case: hey, stop that.