I know that we are not supposed to place private revelations above the Magisterium of the Church or any dogma etc., but how can this be? If the Church approves certain private revelations, how can they be against anything that the Church teaches, or in what sense is it that we can't place them above the Magisterium? Does this actually mean that they are 100% error free, but that no one can be bound to believe in them under pain of heresy/mortal sin/etc. since they are private and have not been "defined"?

For instance, the Dialogue of St. Catherine of Sienna, which it says was "dictated by her in a state of ecstasy" and that God Himself was speaking to her, but is it possible that certain things found there which God told her, are false, and that it was actually the Devil?

I know something must be wrong in for example Anne Catherine's revelations, since she said there are people on the moon and other planets and things like that, and she also said there are Protestants in Purgatory.

I know that we are not supposed to place private revelations above the Magisterium of the Church or any dogma etc., but how can this be? If the Church approves certain private revelations, how can they be against anything that the Church teaches, or in what sense is it that we can't place them above the Magisterium?

When the Church "approves" a private revelation, all that that means is that the Church (generally the bishop of the diocese where the alleged revelation was received) has determined that the revelation was supernatural in origin as far as humanly possible to determine, and contained no errors against faith or morals. Doesn't mean that what was said was necessarily true, just means it didn't contain any heresies. That's why you don't have to believe it, although experience has shown there is significant benefit to be received from many of them.