As far as the every-day running of the city is concerned it is really run by the Council of Representatives, which is a quasi-democratically elected group of people who are supposed to represent their particular group, whether it be a guild, ethnic group, religion or just about any other group of individuals. Just about any group can petition Szen for a representative in the council and the dragon is somewhat (in)famous for accepting any proposal with a large enough backing (100 or thereabouts, depending on the nature of the group), to the extent that Twinfalls has a Representative for the various brothels and prostitutes of the city as well as one for its homeless. Just about the only two sorts of groups forbidden from representation are criminal groups (such as thieves guilds) and cults of Absylus, although that isn't to say that those groups don't try to influence events in Twinfalls.
Although Szen leaves most of the actual running of the city to the Council he does occasionally pass his own laws/carry out his own edicts (or rather, decides to do something which is then made law by the Council) which are equally likely to be reasonable and/or effective as they are to be ridiculous and/or disastrous. For example, it was Szen who devised and constructed the beginning of its sewer system (which has since been expanded to most of the city), greatly cleaning up the water, but he was also responsible for (briefly) flooding a large section of the city because he thought it would make transporting goods around it easier. Long-time citizens of Twinfalls are, in general, used to these eccentricities, although it often catches visitors off guard.
As a result of this, Twinfalls is often called 'The' Cosmopolitan city, with no outright majority to its population in terms of ethnicity or alignment although the city itself is famous for its neutrality to the extent that it has been officially recognised by every major nation and religion (with the exception of Absylus) as neutral ground, meaning that if any nation or group were to attack Twinfalls then it would open itself up to being attacked by just about everyone else.
Twinfalls' defences mostly takes the form of various greatships, the numerous mercenary companies that are based in it and Syanezis himself, although in practice they don't really need to do much as due to its diplomatic status as a neutral territory, no other power has even been foolish enough to attack it.
Being a large city ruled by a Demi-God of knowledge, it is hardly surprising that Twinfalls boasts one of the largest varieties of academies, libraries and other centres of knowledge in Triumve although Twinfalls is particularly known for its innovation. In fact, Lucanus Laethe, the creator of machin, studied and lived in the city for some time and even cited it and some of its citizens as part of his inspiration. Since then Twinfalls has fully embraced machin just as it does just about everything and is without doubt the centre of such knowledge outside of the Savian Empire (and some believe even inside the Empire).
Twinfalls' overall infrstructure is nothing short of wonderfull and bizarre in equal measures. Moreso than even the Savian Empire, it has taken to machin, using them to move goods and people from the various levels of the city, including up and down the two waterfalls that give it its name. One of the more spectacular results of this is its use of machin to move ships from the summit of its uppermost waterfall to the river at the base of the lowest waterfall, where before ships had to dock at river ports at the summit to offload cargo which would be taken by other means to a port at the base, where another ship would usually be waiting to take it the rest of the way.
The bizarre comes from Syanezis' constant tinkering/meddling, from its advanced sewer system to having once flooded half the city to experiment with 'improved transportation'.
Twinfalls itself, as the name suggests, sprawls in-between and around (as well as above and below) two large waterfalls of the Crystal River, which is the largest and longest river in Sanctuary. This makes Twinfalls not only one of the largest cities in Triumve but, save for some of the Sky Island cities, the city with the largest difference between its highest and lowest points, as much of the city is built into the cliff-face of the two waterfalls and the surrounding hillsides, as well as the (relative) flatland at the base.