IOS – How to fix iPhone no longer loading css on webpages and not connecting to internet

Have you tried resetting the network settings with iMessage turned off?

To reset your network settings, tap

1. Settings > General
2. Then scroll down and tap Reset > Reset Network Settings

When the device restarts, turn on your iMessage again and let it activate.

1. Yes, it is possible to have several iCloud email account on your single iPhone 5. You cannot have multiple Apple ID's on the same phone, but can have many email accounts.
2. No, you really cannot iMessage from multiple iCloud email accounts. That said, it is technically possible, but would require going into the Settings app every time you wanted to message from a different email account and would prove to be quite cumbersome to setup. Even then, they could easily message your other iCloud accounts that were linked to messages. This could quickly result in your having several message threads from the same recipient - an unfortunate situation.
3. Yes, you could technically set up a rule that would forward emails received from the Coworker to another email. Then you could set up that email to automatically tag or mark emails from that iCloud account as read or whatever was needed. It would not be possible with iMessage.

Honestly, it sounds like coercing iCloud and iMessage into what you need is a little too much for what it was designed for. While it may be possible to figure a solution out, it is more likely that you could find a third-party solution that would suit you well. Case in point, Google offers Gmail and Hangouts which would allow for emailing and instant messaging - all for free and with associated apps if desired. There is chat history and emails can be archived forever.