Secret Vatican Archives

1. The Gnostic gospels are not secret. They are available online
2. They say nothing about the "lost years". By and large, they are "sayings gospels"; they ascribe various sayings or teachings to Jesus, but they don't give biographical information, or accounts of what he did; just what he taught.
3. Why would the Vatican posses the original copies?

The "Vatican Secret Archives" are secret as in private, not secret as in mysterious hidden knowledge. They are the kind of secrets that a secretary keeps. They contain administrative records - accounts, correspondence, reports - not scriptural or theological texts (those are in the Vatican Library).

They've been open to researchers since the late nineteenth century. There is still a closed section that cannot be accessed without special permision, but that contains the very newest records, relating to business still ongoing or to people still alive or only recently dead, not the very oldest.

The Third Secret of Fatima isn't an early Christianity thing, though. Completely a twentieth-century business.

Esoteric speculation about what's in the Third Secret of Fatima is hampered by the fact that the whole thing was published, in full, in 2000, and Google will take you there in two shakes of a lamb's tail, if you're interested. But that kind of transparency has never bothered the manufacturers of conspiracy theories and the devotees of secret knowledge.

There is part of it, as Peregrinus says, very easy to google. The bit about Russia is to do with various popes consecrating Russia to Mary, again easy enough to check up and find the version you wish to read.

There is no reason to think so.

It was the Apostle St. Thomas rather Jesus himself who was rumoured to have traveled to India in 52 AD to convert people to Christianity:

https://en.wikipedia.org/wiki/Thomas_the_Apostle#Mission_in_India

https://en.wikipedia.org/wiki/Saint_Thomas_Christians#Tradition_of_origin

How would Cardinal Ciappi have known what the Third Secret was?