Hmm, 'republic' and 'democracy' are different things, but they are not mutually exclusive, are they? They simply refer to different aspects of the constitution. The Netherlands is a monarchy and still democratic; the US is a republic and also democratic. What kind of electoral system is fairer is a matter for discussion of course - I always like the fully proportional one best - but in general both countries are considered democracies.
Just to avoid stupid confusion, I would take the following approximate definitions:
republic - president as head of state;
monarchy - monarch as head of state;
democracy - 'that institutional arrangement for arriving at political decisions in which individuals acquire the power to decide by means of a competitive struggle for the people’s vote'

... that's a definition by Schumpeter written in 1943 (in political science there is this big debate whether this is enough, or you need some kind of concept of liberalism in it as well ... but I like this clear definition better).
About the English court system: I must admit that I am not 100% sure about what I said. I simply cannot imagine that there would be a respected democracy where the accusor does not have to prove the accused is guilty. Maybe I was just naive

... It sounds scary to me if that were the case. But this came up referring to Quillanoi - how would it be the case there? Yes, people are detained before there is solid proof, but the US police also arrests people before the court case is done, not? The main problem is Quillanoi is simply the inactivity of the Senator (due to the player being absent, albeit eager to start playing again) and the court cases are postponed too much.
It is interesting to read all those things about political systems in Cantr. As said many times before, that is one of my key interests when I created the game, and I am really happy there is indeed quite some diversity in systems. It is indeed striking how influential companies are, but I am not sure this is that different from how it has been in the real world. At least the Dutch 'Verenigde Oostindische Companie' (VOC) was really powerful in all Dutch colonies in the 17th century. Are there more real life examples?
And about the companies in Cantr, I think the Cult Mechanicus in Quillanoi is also fairly close to running the city. They don't make the laws or run security, but they are by far the largest employer and have the most developed regional system. But I hope there will be some more competition in the future

...
Are there other democracies in Cantr that are somewhat similar to Quillanoi? Where there is a constitution?