Sedevacantism is a movement within the catholic church that fully rejects all changes made by the second vatican council (e.g they still practice mass in latin, old forms of preyers, they reject ecumenical dialogue with any other religions and reject involvement of secular people in the liturgy).They have their own organizations, like Opus Dei, their own media and invest their own capital into their church.

The movement is not big in numbers, but they are influencial in many catholic countries and have their own people in mainstream church organizations and in the Vatican. Sedevacatists have been critisizing the current pope for years, accusing him of being too liberal, and thus pulling people away from being saved. Examples of him being too liberals include actively trying to invite gay people to church or involving more woman into the liturgy.

The movement is expressing their critique through their own and mainstream catholic media.

To the best of our (CAP) knowledge, the Pope is still alive. 

one-country-VETO rule" is a rule of the EU which states that a proposed policy or directive of the EU can be VETOed by a single country in the EU. This rule does not apply to all policies and directives but usually only applies to matters of high national interest (e.g foreign policy, defence, enlargement of the European Union, finance and amendments to treaties)