Will Solidworks Educational Edition 2016 and / or 2017 open an assembly model created on Solidworks (professional) 2010?

You should be able to open the SW2010 file, although going back that far you might get errors.  However, once it's been opened and saved with the newer version you won't be able to open it in SW2010 again.

I've never used the Student Version, so I can't answer the pdf question.  I'm sure someone else will be able to.

Yes and yes.