Are you referring the the "Messages" Folder? That is a catch all folder, it will catch all incoming email messages (from any account), SMS, MMS, Calls, PIN messages, etc. You can hide this icon, but not delete it.
You can separate SMS from this by going to Messages > Options > General Options > SMS & Email = Separate.
You can separate phone logs from showing there also by going to Call Log (green key) > Options > Call Logging > None.
As for the mute button, there is a fix for that here : Fat Face Fix !!