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.
I studied the information you gave me. First of all, the finding of something written decades or even centuries after a person’s death does not necessarily mean it’s a forgery. St. Louis De Montfort’s writings were discovered decades after his death. Even among secular writers, how many were unknown during life only to become famous after their deaths? Because of the VAST amount of paper work the Vatican has, it doesn’t surprise me when they find papers even centuries after they were written.
Also, I don’t think the prophecies are that “vague”. De labore Solis (Labor of the Sun or Eclipse of the Sun) seems to describe John Paul II. A former laborer who labored hard for Jesus, there was a solar eclipse visible in the Americas during his funeral, April 8, 2005.
John XXIII is described as Pastor et Nauta (Pastor and Mariner). Knowing the prophecy, one of the cardinals sailed to the conclave trying to send a signal to his fellow cardinal-electors that he should be elected. He wasn’t, the former Patriarch of Venice (a city built on the water), Cardinal Roncalli, was.
Paul VI is referred to as Flos forum (flower of flowers). He had 3 lillies on his coat of arms.
Again, people can have their own opinions about the prophecies. But IMO, they have not come close to being “proven” false.