What are the rights to exported video from the Apple's Keynote app?
This is really going to come down to what the terms of the EULA is.  It should outline what rights you have to use the Apple provided contents.  Most likely you would be fine as included assets are typically intended for reproduction.  It might be trickier if you were going to sell copies, but a commercial is probably ok.  

As far as using it as commercial work, I'd be careful about what you use it for.  The quality level is still probably going to be sub-professional for most purposes.  Programs like Keynote and PowerPoint are really more designed for making basic presentations easy for the average consumer rather than trying to actually make a good commercial production.

It is also worth mentioning that while the classical music itself may be in the public domain, the particular recording may not be.  Rights are a complex thing and while classical music in the public domain is free for anyone to play, copyrights can still exist on particular recordings that have been done recently.  Unless you specifically purchased it as royalty free from a reputable dealer, then you may want to double check that as well.