Dear Konrad:

The Rosary is personal devotion and thus the Church does not regulate it. The custom of praying a particular decade on a particular day is just a common custom. Thus, people can pray it anyway they wish, or pray whatever decade on any day they wish.

Liturgically St. Patrick's Day is an "optional" memorial. As such, celebrating that feast is never mandated by the Church, but it may be mandated in a diocese, parish, or religious community with St. Patrick as their patron.

But, even in those dioceses, parishes, or communities who have St. Patrick as patron, that feast cannot be celebrated during Holy Week since the weekdays of Holy Week outrank an optional memorial or a even a feast of a patron of a diocese, parish, or religious community.

The Feast of St. Patrick may be celebrated on Friday only in those dioceses, parishes, or communities where St. Patrick is the patron. For the rest of us St. Patrick's Day is an optional memorial and thus cannot be celebrated on a Friday of Lent.

All this is speaking of liturgical celebration. These rules do not apply to non-liturgical and secular celebrations.

As to which decade of the rosary to pray when praying on a Solemnity the custom may be to pray the Glorious Mysteries. But, again, there are no regulations on the Rosary so you may do whatever you feel prudent.

God Bless,
Bro. Ignatius Mary