Can this be done?
Would it be possible for the site to add a feature such that when I type the first letter of my email address into the sender and recipient lines in a message, my email address pops up and I can click on it to insert it so I don't have to keep typing my email address over and over?
I'm guessing you mean when using the Email link to send a page to someone? If so, if you're logged in when you do that, it should populate the sender field with your registered email address.
The recipient is assumed to be someone else, though, rather than yourself, so it doesn't populate that.