This is sort of a “cliché” question, but if an apparition is approved by the church (e.g. fatima), does it mean that the apparition is definitely true, or does it simply mean that the church could not find any feature in the apparition which contradicts the church teachings? What if (this is just pure and random example) the church 50 years later finds out that the lourdes apparition for example was false after all, even if it was approved for a long time, would this piece of evidence invalidate the church?
The answer to your hypothetical question, is no. It would serve only to invalidate the presumed validity of the apparition in question.
What the Church does wrt to apparitions is not to ‘approve’ them, per se, but rather issue essentially an official ‘negative approval’–which is to say, that after thorough investigation, nothing about the apparition contradicts Church doctrine, and nothing was found to disprove the claimed apparition. As such, Catholics are free to accept the apparitions as being genuine, and for devotional purposes.
If later evidence came out exposing a claimed apparition as a fraud (for instance; or a result of dillusion, or what have you)–the Church would reverse the ‘negative approval’, and state that it is no longer acceptable for Catholics to treat the said claimed apparition as genuine, and at least any aspects found to be contradictory, would not be acceptable for devotional purposes.
It is worth noting that this is how Catholicism works in general–aside from the affirmative declarations of dogma, most any belief or holding that does not contradict dogma (or otherwise contradict official Church teaching, or Church position), is essentially fair game. This is why you have many ‘radical’ groups within the Church, that are not [necessarily] heretical, but then, not exactly ‘sanctioned’ either. e.g.–charismatics, and some of thier beliefs wrt to ‘speaking in tongues’ and the like. The Church may not necessarily approve of their claims, or officially ‘sanction’ them–but as long as they are not expressly contradicting the Church, they can remain Catholics in good standing.
E.g. 2–Case in point wrt to ‘apparitions’: Medjagorje. Not approved. In fact, essentially ‘disapproved’. Yet, to the extent that those
apparitions do not contradict Church teaching, it is acceptable for Catholics (individually) to use them for devotional purposes and pilgrimages there–(but not through parrishes or the like, as that would be tantamont to tacit approval).
This is of course ‘broad brush’, and others will likely disagree to differing degrees with my characterization–but I think you’ll find that for the most part, as a general analytical framework, it works.
CAVEAT: of course also, this is just one humble poster’s opinion/take on it; not intended as authoratative, and I certainly welcome any dissent, or clarification.