[Stephen Metzger]"I'm on an early 2013 MacBook Pro running OS X Yosemite"
That's why. FCP 7 isn't supported under Yosemite. Full support for FCP 7 stopped at 10.8...actually, I think before that. 10.7 was in play when FCP 7 was discontinued, and no longer supported by Apple. OS 10.8 worked fine...but really, from that point on they didn't take FCP 7 compatibility into consideration when making later OS versions.
You might check your Power preferences and make sure that your external drive isn't spinning down or going to sleep while you are using a different application. It sounds like FCP might be waiting for the drive to spin back up before it responds.