Short answers, pulled from the story.
Lucius Junius Brutus and Collatinus expelled the kings from Rome to establish a system they called res publica. This Latin phrase meant public thing and described a government where sovereignty resided in the people rather than a hereditary ruler.
Italy became a republic after an institutional referendum held on the 2nd of June 1946 marking Festa della Repubblica celebration. Giuseppe Mazzini founded Young Italy movement in exile in Marseille during July 1831 aiming to transform Italy into a unitary democratic republic before this date.
The Corsican Republic lasted fifteen years from 1755 to 1769 before falling to Genoese and French forces under Pasquale Paoli who led reformers pushing for political overhaul through constitutional and parliamentary means. His government introduced universal male suffrage and granted women voting rights at a time when French women could not vote.
James Madison rejected pure democracy in Federalist No. 10 calling representative democracy a republic instead because he argued what distinguished democracy from republic was that former weakened as it grew larger suffering violently from faction effects. He believed a republic would prevent majorities from trampling inalienable rights like life liberty and pursuit happiness.
Thomas Paine's Rights of Man sold over forty thousand copies in Ireland within eight months of publication during an uprising against British rule lasting from May to September 1798 with military support from revolutionary France. The Society of United Irishmen founded in 1791 in Belfast and Dublin identified English rule as corruption threatening Ireland's liberty before this period.