Does auditing a course hold any value?
Many of your questions (about edX) will be answered by Wikipedia. Whether you can get transferrable credit for any course is up to the individual institution who might accept such a course or not. I don't know, but doubt, whether and institution would tell you before you take such a course whether it would "count". 

However, it is a potentially viable resource for learning. But that depends on what  you actually do in the course, not just what you see or sign up for. If the course provides you sufficient practice and feedback on your efforts then you could learn something, even if you have no  visible "credit" for it. 

Audits, even in face to face instruction can be valuable provided that the student does the work and gets appropriate feedback. 

And even if you "purchase" an entire course there is no guarantee that a university will accept what you have done. It is pretty risky for certification, even if they issue "certificates". However, the sponsoring institutions (MIT and Harvard) are reputable, so there is likely less risk than if it were run by "Dr. Buffy's Online Diploma Mill". I'm pretty sure that one is disreputable.