I have a MacBook and unless the school has majorly locked down her MacBook Air, it should be a relatively trivial thing to play mp3 audiobook files on it.
If you're using iTunes, all you have to do is to drag and drop the files onto an open iTunes window (plain mp3s require no conversion at all) and it should automagically add them to the iTunes Library. You may want to fix the ID3 tags on the mp3s if they're not set correctly, and you can do that by selecting the tracks and doing Cmd-I (or File --> Get Info from the menus).
From there you can fill out the author/reader/etc. names properly in Details, and then under Options you can switch the Media Kind to Audiobook and check the box for Remember Playback Position, which will make iTunes (and any syncing iPods) remember where the track was last paused and resume it there for playback next time, IIRC (it's been a while since I ripped my audiobook CDs to the computer, so I'm a little fuzzy on what exactly I did last time).
It's also possible to join the tracks into one single file with bookmarkable chapters and do other advanced tricks.
If iTunes seems too unwieldy for just listening to audiobooks, you can play pretty much anything with
VLC Media Player,
X Lossless Decoder will rip/convert a whole bunch of file formats, and
Tag will help you fix tags for many more formats (ETA: maybe not for MP3s, since I generally do mine as FLAC and then set the tags and convert, but properly filled out ID3 MP3 tags will be automatically recognized by iTunes anyway).
(ETA: also, it's possible to play mp3 and other media files right from the Finder, if it turns out she really can't add anything to her MacBook Air and has to run stuff off of a USB drive. Just set it to Column view, select the file, wait for the little preview to load, and click the play button. Just don't click away from that particular file in the Finder window while you're still watching/listening to stuff, but opening up other Finder windows and keeping your "listener" in the background works just fine.)
Incidentally, the way to open applications that are not signed by the Apple Store is to Ctrl-click on them to get the menu for Open, which will bring up a "warning dialogue the first time saying that this is an unrecognized developer do you want to proceed?" and once you've said yes, they should open just fine by regular double-clicking the next time. (There may be some kind of advanced setting to prevent this for non-admin accounts, though, but it can't hurt to give it a try to see if it works on hers.)
Hope this helps.