Press on "elite*gold" at the top of the page. There you can see all your trades.
At the status of a trade you can see if the other person accepted your request or not.
The status is either "pending" or "successful".
Private messages are safed up to a certain number (which you can see under the "Folder controls" when you go to your inbox) and got deleted after 3 months.
When you want to safe more and don't want that your messages got geleted after 3 months, you can buy premium membership (1000 safed messages) or elite membership (100,000 safed messages).
Another option is to download them (at the bottom of your inbox).