This stems from the Lateran treaty that setup the legal relationship between Italy and the Vatican. Certain employees of the Vatican are made citizens of Vatican state for the period of their employment. However, this citizenship is removed once their term ends. The Lateran treaty refers specifically to this group as follows:
"Ceasing to be subject to the sovereignty of the Holy See, the people mentioned in the preceding paragraph may, if in terms of Italian law, regardless of the circumstances of fact set forth above, are not considered to be equipped with other citizenship, will be regarded in Italy as citizens certainly Italian." (Google translated)
Essentially, former citizens of the Vatican who no longer have any other citizenship are automatically granted Italian citizenship instead of being made stateless. This opens up the tantalizing possibility of the pope hiring large numbers of temporary staff for 2 days. Then, once they have renounced their previous citizenship- firing them- making them automatic Italian citizens. This logic suggests that the Pope can essentially create as many Italian (and therefore European) citizens as he wishes.
However, what would happen next is more murky. Since Italy hasn't signed the Convention on the Reduction of Statelessness, which generally disallows the removal of citizenship when it would leave an individual stateless, they might just pass a law revoking post-Vatican citizenships. I'm not a legal expert so I'm unsure whether this counts as breaking the Lateran Treaty. EU law might also have some sway but it generally defers to Member States on their right to determine rules around citizenship.
1) I certainly don't think Francis will do this and the effects of it would likely be very uncertain.
2) This is basically a "real life" version of the ploy from Elysium to get everyone in the world healthcare.