Hi Muzza -
Seems like you could get most of the way there by combining some tools if you're willing to roll up your sleeves a little bit. You might look into a tool that can convert multiple e-mail accounts into an RSS feed so that everyone can view the e-mails. But I don't know of any single web-based tool that can do all this.
For one thing, some of your criteria are kind of tough. For example, aggregating several POP accounts into one web-based account is pretty simple. But what about sending out e-mail from those accounts? If you have firstname.lastname@example.org, email@example.com and firstname.lastname@example.org, how do you specify which one is the sender? Outlook can do this, but no web tool I know of.
Actually, come to think of it, Outlook plus Exchange Server meets all your criteria. Exchange has some really sophisticated web mail features, plus things like public folders and routing rules that could be configured to make it all hang together. But it's not cheap and it's not easy to set up Exchange + Outlook. Plus it's Microsoft.