I think - though I'm not sure - that something changed in a recent update.
If you use a class from the global scope i.e. \Request, PhpStorm will import the Request alias. Previously importing Request would import the facade itself (at least in my experience).
At least now you only have to enter the backslashed class name once, then import and forget. May or may not have something to do with the fact that L5 is all namespaced, but I couldn't say for sure.
Are you sure you have the action "Show Intention Actions" mapped to "alt" + "return". You can check this in your preferences and search for "keymap". If you click the search/loop icon you can press a key to find the binded actions.