Wait a minute - the Papal States, despite their name, were neither a federation nor a loose condfederation... quite a single unitary state instead! It couldn't have warred against itself. However, it is true that cities such as Ferrara became part of it after a (bloodless) conquest; San Marino was actually almost annexed in 1749.

And no, actually the Papal States didn't have neither a stable army nor mandatory conscription for much of its existence - this is something that took place only after the Napoleonic conquest of Rome. But the Papal Army had, throughout its long history, a truly enormous amount of units and specialities many of which were little more than short-lived experiments; its backbone was naturally the fanteria di linea ponticificia, whose early 19th-century uniforms looked like this and this (the latter's a corporal). Other rather famous units were the dragoni pontifici - which also acted as law enforcement, being tasked with hunting down the brigands hiding in the countrysisde - engineers, artillerymen, and the like. However, after 1860, it was mainly foreigners who were entrusted with the defence of what was left of the Papal States; the Zouaves served the Pontiff until 1870, when Rome was annexed by the Kingdom of Italy.

You can find more uniforms here: http://www.araldicavaticana.com/divise_ex_esercito_pontificio.htm

Surprisingly enough, life in the 17th-19th century Papal States was pretty much like life elsewhere in Italy. Romans in particular were known for being rather unruly and each ward (rione) of the city had an intense rivalry with one another - Trastevere hated Monti, Monti hated Trastevere with a passion ^1, etc., etc... breccolate, stone fights among youngsters from different 'hoods, were rather common and usually took place in the Forum... whose ruins often served as ammunition! ^2 These are well detailed in both Giuseppe Berneri's poem Il Meo Patacca and Giovan Camillo Peresio's Il Jacaccio, overo il Palio conquistato.

Religion was naturally a feature of everyday life and was held in high regard, but there were also more 'pagan' forms of entertainment such as the Carnevale, in which horses would have been made to run through via del Corso and then the contestants had to stop them with their bare hands (many lost their lives trying to do that, and this is exactly why the celebration was banned in 1883) or the Quarantore... a more 'serious', yet pompous, carnival which took place during the forty hours between Christ's death and His resurrection. Other important feasts took place on June 29th (St. Peter and Paul) and the 15th of August, ferragosto. Public executions were also occasion for social gatherings and these usually attracted big crowds as they were extremely cruent; many were carried out with a hammer (mazzolatura) or, after the early 19th century, a guillotine.

Law enforcement was the duty of a rag-tag - and, arguably, ineffective - militia, which would later be reformed as the Gendarmeria Pontificia in 1816; the countryside itself was rife with brigands and highwaymen. Literacy was definitely not not widespread, with most people being illiterate; letter-writers and notaries were thriving as their services were very requested. The Church, through the various religious orders, took care of the citizens' health by means of 'hospitals' run by them. As far as industry was concerned, it saw a very limited growthduring the latter half of the 19th century and the rail network was not very extensive as well, mostly connecting the capital with the so-called Castelli Romani and Viterbo; and most people were either farmers or artisans. Finally, the Jews were forced to live in a small, walled ghetto near the river (which was prone to flooding) from 1555 until 1852 and then again until 1870. But despite all these hardships, life then was much more gaudy than one would be led to assume.

Of course there was also a nobility, whose most important families (the Barberinis, Orsinis, Colonnas - just to name a few) all resided in Rome and more often than not, hated each other. But there were also other houses, mainly in what are now the Marches and Romagna - Giacomo Leopardi came from one such faimilies - some of whom even had Jewish origins (such as the Pierleonis); many of them rose to fame because one of their family members was elected to the Papal throne, and many of the honorific titles at the Papal household were very sought after. Until the late 16th century, these families often engage in bloody feuds, during which the population was also involved - each ward of Rome was governed by a caporione ^3 (some kind of neighbourhood mediator/facilitator, whose term lasted six months) who usually took orders from the most notable family in the 'hood and many citizens also enrolled in their private militias, so clashes between rival bands were not at all uncommon.^4

 

Edit: I've modified the post in order to include the sources.

^1 Giuseppe Baracconi, I Rioni di Roma, (ed. Roberto Napoleone, Roma 1986).

^2 ibid.

^3 ibid.

^4 ibid; Anonimo Romano et al., Cronica, (Adelphi, Milano 1979), ch. II-III.