What free online educational resources should pilots in training be aware of?
The Airplane Owners And Pilots Association has lots of great articles on both training and new legislation that comes down the pike. The new information is really nice as it lets you know what may be or has changed since the last time you studied the books. Its worth it to join as well (its less than $50 a year and if you have just started to train they are about to bombard you with mailers anyway). 

Along with publishing the FAR's the FAA publishes lots of Briefings and really great supplemental material and handbooks like this one on airspaces. 

There are lots of Youtube channels out there with great information like FlightChops and the like, but note they are not in any way approved training and may not cover every aspect of what they are doing. 

I like to read GeneralAviationNews.com. Its a nice source of informative articles on what is happening around general aviation, airplane ownership advice, mechanical engine advice, and all all manners of legislation that are being discussed as well as fun fly ins and things like that.