I think it's impossible to find, free, online classes that can fully replace the function of a good teacher.
However, I have tried to make a website (designed especially for the Italian language, 'cause I'm italian, but can also be used with the English language) to allow free for everyone to improve with a course of study organized from scratch or at least from a low level and going beyond .
I'm not a pianist but only a beginner, but I count on the fact that, on the site, can be added the contributions from someone skilled and willing to help beginners.
The site is here:http://www.corsodipiano.altervista.org/
The English version (to be updated) is here:http://www.corsodipiano.altervista.org/indexe.htm
In this site you can find sheet music and many methods, tens of thousands of pages and thousands of midi files, organized into several levels and is provided for the registration of youtube channels of the pieces.
I'm happy if someone wanted to try to use this website, even if only to download the sheet music and methods, and if someone wants to write on the forum for comments, suggestions, or if you would somehow help the initiative.
I look forward to some answers about.