If a friend sends you a request for an item, you'll get an in-game notification the next time you log into the game. Sending the requested item to your firend is as easy as simply acknowledging the request.
Notifications just become part of your inbox. Once you click OK, all messages are answsered. The roster may be longer than you realize, but you can scroll through it to see all the help requests, coin/energy gift notices, etc., if you really want to read them all.
I play through face book and I have never seen a letter icon on the screen. Occasionally there will be a round icon on the lower left of the screen above the energy icon and below the puzzle icon with a request. Once I accept it the icon goes away. So I have never been able to see the actual inbox.
Here are some screenshot from my game. Note the icons from the left side of the screen. The INBOX is round with an envelope (letter) and an orange star which shows how many messages I have. When I click on it, I get the pop up window (see below) showing my "INBOX". The blue arrow points to the scroll bar. If I click the green button to "ACCEPT AND SEND," all gifts will be accepted and all gifts that friends requested of me will be sent. Then the icon and inbox window will disappear.
The your friend receives a request for a collection item, it is automatically given once they accept . Even when they are exceptingenergy tickets etc . Once they click accept and send, you will notice the item checked in your collection as received.