How can I quickly play the selected song in iTunes, without playing the rest of the album?
One option would be to save this script to ~/Library/Scripts/Applications/iTunes/ in AppleScript Editor and give it a shortcut with FastScripts.

try
    tell application "iTunes"
        play item 1 of selection with once
    end tell
end try


Without the try block there would be an error dialog if for example the selection was empty.