Q. 1. At some Catholic Churches, during the Holy Mass, some of the people hold hands during the "Our Father" prayer. Is this something new that the Vatican has introduced?
A. 1. The holding of hands during the "Our Father" prayer during the Holy Mass is not part of the Catholic Liturgy. It has never been approved by the Vatican. Such a practice and/or any other practices that are not a part of the Catholic Liturgy should be discouraged and discontinued.
The Vatican goes through much effort to ensure that the Holy Mass, with the exception of the language, is uniform (identical/consistent) throughout the world. In other words, if you were to travel to any country, the Holy Mass in that country, with the exception of the language, should be no different than the Holy Mass that is celebrated at your local parish.
Unfortunately, some priests, not out of ignorance, but in total disobedience to the Vatican, introduce strange practices during the Holy Mass. And what is sad about this is that many bishops are aware of these strange practices during the Holy Mass and they remain silent to them.
I personally know of one Diocese where the abuses of the Liturgy as so great that you can easily identify each different mass with a specific priest. The liturgy of the Holy Mass is not uniform (identical/consistent) throughout the Diocese.