How can I view the full headers of a message with Outlook 2011 for Mac?
The only way I've found is to right-click on the message in the message list and choose View Source in the popup menu. This will open the full source of the message, including headers, in a new TextEdit document.
On any Mac, holding down the Control key and clicking is the equivalent of right-clicking on a PC. It will usually bring up a contextual menu that shows choices of actions available for the element that is selected at the time.
To see which e-mail address an e-mail was sent to, open the specific e-mail, then hover over the alias in the e-mail header's To field. A pop-up will expand to show the actual e-mail address tied to that alias.
Seeing the full e-mail address of the sender is a little more complicated, because hovering over the From alias usually displays only a truncated portion of the actual e-mail address. The same can happen if you hit Reply (with the intention of deleting the Reply e-mail before sending it).
However, if you hover over the From address, a pop-up window will appear, with a number of icons along the bottom. The icon all the way on the right (picture of an index card) will open an Outlook Contact form, where the full e-mail address of the Sender will be displayed. Once you've viewed the e-mail address, close the Contact form and choose Don't Save (unless you really want to create a contact for that sender, in which case, hit Save). Sounds complicated, but only takes a few seconds.