I say there should be not only the Inbox section on the messages, but there will be outbox (So I can see messages I sent people and if they've opened the message already).

In additon, If there is a buddy list on Toribash and one of my buddys is online on the forums - there should be an feature to have a kind of messenger on the forums so we could contact each other live (Private live chat, kind of).

There is already an outbox, jut click the arrow next to the box that says inbox and select 'sent items'

For your second idea there is things like steam, skype etc.

Helped me with the outbox, thank you!
Cheers