They haven’t been “proven to be fake”. Catholics (and anyone else) is free to believe them or not believe them.
They have indeed been shown to most likely be a forgery. See here, paying special attention to points 5-9. The whole article is beneficial really.
Catholics (and anyone else) is free to believe them or not believe them.
I suppose in a certain sense you are correct (as far as Catholics are concerned at least) since the Church hasn't specifically condemned them, by name, but reason should inform and prevail here. I submit the historical evidence Akin lays out in the site I provided makes it reasonable to say they have been "proven false". At least as much as any historical (or prophetic) claim can be falsified.
Anyone can believe anything they want. Especially when talking about vague prophecies such as the ones attributed to St Malachy. But it really profits no one (no pun intended) to give them any merit.