He taught a class, and yes it was sponsored by the church. (But if you know so much about this, surely you recall that Jackson sent funds himself from the field back to Lexington for the school.)
So what if black sunday schools were common throughout the South? Why would that diminish the fact that it was a very different situation from what is often portrayed in Northern grade schools today? It only illustrates my point more.
And yes, it was for both free and slaves...again, even slaves were taught (which conflicts with what was taught to me in grade school). And the sources I have seen have pretty clearly indicated that reading WAS taught...else no mention would be made of him violating laws against teaching blacks to read! Where are you getting your claim?