What are some free legitimate proofreading courses online, with a certificate after course completion?

The problem here is that you expect to find a quality course for free. If you expect to learn all the information required, you are going to have to spend some money. Simple courses, even with certification will not get you there.

I would consider the kind of work you want to get, the sort of places where you might want to have these skills and see what they expect from their proofreaders. You will likely find what is required there as to the kind of training.