Right. More setting comments! The population is slowly growing and nowhere near capacity; trade between worlds is expensive, since populations are tremendously huge and ships can be expensive, and so is largely in luxuries and a small number of very important goods. Planets blockaded by the Black Fleets experienced economic troubles and had to scramble for solutions but succeeded in finding them, with their lifespans not significantly decreasing under occupation. "This is, of course," he says drily, "why so many of them seceded; they could manage without the royal government, did, and saw no reason to resume paying taxes afterwards. They are not especially happy with the - de facto - answer of 'the Royal Fleet.'"
Ships are constructed in orbit, at specific starbase-factories, with most of the metals used to make them coming from asteroid mining. Civilian ships are usually sponsored by major merchant corporations that can muster the resources to build them; military ships by the great lords and the Crown, with the largest fleet by far belonging to the Crown. The actual work is largely carried out by skilled and talented craftsmen, shipbuilding being considered the most prestigious non-noble career.
FTL consists of rare stable paths between systems through 'hyperspace', which are quite small on astronomical scales though huge compared to, say, a person; lanes are of varying stability/ease of navigation, anything leaving the lanes is lost forever (a fatal process), and the Black Fleet's ability to navigate difficult unstable lines is only now being equaled. Technology to stabilize and carve new lanes is possible by the laws of physics but at least a hundred years to prototyping, and probably much slower at the speed Villarosa is progressing at. Ships traveling on these hyperspace lanes may encounter each other unexpectedly, triggering battles if the ships are hostile, but since this environment is extremely unsafe as many battles take place in systems as outside it. Only ships with the required large and expensive piece of equipment can enter or leave (or survive) hyperspace; hence the importance of carriers, which can secure escorts from the dangers of the travel method. Leaving hyperspace can put you in a fairly wide area outside the gate, somewhat unpredictably, limiting the ability of the attacker to simply mine a known exit.
Full-scale warfare on the ground essentially never occurs; orbital bombardments would defeat any ground-based threat but are not used because there is a clear consensus that if you would be orbitally bombarded you instead surrender. When there's ground-based fighting it's either duels between nobles (in which case the stronger psychic almost always wins) or attempted assassinations or bombings, or troops taking control of territory opposed by guerillas who didn't obey the surrender notice.
The legal system varies depending on the individual region - most planets take care of their own affairs, and their ground-level legal systems do not particularly impact the adventures of spaceborne aristocrats or aristocrats-to-be, but all nobles have the right to appeal to their liege-lords for crimes committed by them or against them, and, ultimately, to the monarchs (who may decline to hear the appeal, but who always have the right to). Noble courts go by traditional methods of determining the truth that are sometimes just copying what local systems are doing, which can work well, and sometimes frank exercises in aristocratic power to decide the "right" answer, ie the one more favorable to the aristocrat; they sometimes use trial by combat to provide a pretense of fairness in what the judge who chose the method knows perfectly well will be the execution of a weaker claimant who dared to challenge the nobility. "In the interests of keeping the ineffable Will of the Multiverse happy," he says drily, (and to let him import his preexisting skills) "symbolic, psychic-assisted swordfighting is common as a mode of duels, since you can channel your psychic powers through a sword and cannot thorough a rifle."
(Sandor is well aware of what the nobility tropes in Roses of Villarosa are supposed to look like, and is prepared to play to them.)
The most common ground-level options tends to vaguely resemble Anglo-American jury trial systems, since this works fairly well, but there's a wide variety between worlds and between jurisdictions on individual worlds.
Advanced technology in common use does not include any mind-reading or (at all reliable) truth-detection machines, but does include cameras. There are no robots smaller than medium-sized birds, and miniaturizing them further is quite difficult; artificial intelligence is tremendously expensive and there is a reasonable expectation that it will stay this way forever; people-quality AIs require huge amounts of money to construct, and cannot easily copy themselves, and although manual-labor machines you could call robots exist, the line between those and any other manufacturing technology is not very sharp.
There are system-wide internets and ship-related internets, and near-total internet anonymity; the easiest way to discover someone's online identity is to get video evidence of them and their computer screen together. This does not work very well on psychics, who can interface with the computer without touching a keyboard or looking at a screen that anyone else can see.
Scientific progress on ordinary planets is usually limited to commercial uses, which includes medical technology or healing drugs for sale; science is also sponsored by monarchs or nobles for their specific ends, most of which are military - specifically, the construction of more advanced ships less expensively. There is very little research into non-applied science or social science except insofar as governments think it serves their purposes.
(So far no equivalent of heroin has been invented and the entire line of research that is dangerous addictive drugs is correctly considered a dead end. Even their painkillers are nonaddictive.)