Short answers, pulled from the story.
Count Floridablanca and Count Campomanes rejected claims of inalienable Church rights in secular matters. Bourbon monarchs implemented regalism policies expanding royal jurisdiction over all Church activities except spiritual spheres.
In July 1870 the council issued a Dogmatic constitution defining four doctrines of Catholic faith. These included apostolic primacy conferred on Peter and perpetuity within Roman pontiffs.
French Catholics used ultramontain to describe supporters of papal authority within French affairs. Opponents labeled these individuals as lacking patriotism and serving foreign interests over national ones.
Cardinal Henry Edward Manning became one of strongest advocates for ultramontane position. He believed unity and discipline protected church interests within liberal democratic states.
Specific declarations appeared in Munich Congress Declaration, Theses of Bonn, and Utrecht Declaration documents. These texts formed foundational basis for Old Catholics who split from Rome over infallibility and supremacy dogmas.