Are there civilian courts? Starfleet are the police and they are Prison Guards. The Doctors case about Intellectual Rights was presided over by an admiral. Is it possible that Starfleet is the entire Federation legal system?
Seven's changes or lack thereof are totally plausible and even likely given her character. They've done a good job of with her. Seven on VOY was a basically a child. This is the adult version. One question: does she still have to regenerate at night?
If she has implants she should need regeneration. Although, regeneration might look different now. It might be a pill, it might be a small hand held device. She didn't seem to need to build an alcove in season 1. And then Q transplanted her soul into a fully human body. Her implants are new and probably less intrusive and numerous. Her regeneration needs are probably different because of that.
No evidence either way, but that could just be "PoV" bias. . Again, mostly PoV bias most likely. We do know from Homefront/Paradise Lost that Starfleet doesn't normally patrol the streets on Earth. Probably at least in part due to the substantive legal issue being whether the Doctor is "property of Starfleet" or not. In the sense of it being the equivalent of the US Federal court system... maybe, though I doubt it. In the sense of it being the sole legal system for all purposes at all levels... no. The canon has been clear that individual planets remain independent for internal purposes (cf US state law), even if they are largely if not entirely subordinate to the Federation/Starfleet for external affairs.
Conflict of interest. Anyone but Starfleet should be having to decide if Starfleet is allowed to keep slaves, which is what every case with the Doctor was really about. Who was the warden and guards on Alba II? Were they Starfleet? Starfleet Security locked horns with the The Orion Syndicate, who are simple Criminals, not an alien government.
Elba II was a place for the incurably insane, so it was more a maximum security sanitarium than a prison.
Debatable, but beside the point as Starfleet wasn't making the decision. Per the episode: Captain's log, stardate 54748.6. A Federation arbitrator has been assigned to determine whether the Doctor has the right to control his artistic creation. Because of our limited comm. time with Earth, the arguments should take about three days. I'm not sure where you got the idea that an admiral made the decision in the first place? The only admiral who was involved in the process was Owen Paris, and his only role was a project lead of the communications project that facilitated the hearing. Given that Elba II was run by a civilian governor, probably not. Though federal law enforcement or even military personnel being involved in prisons that hold military personnel isn't unprecedented IRL. Yeah, that's like saying that the Bratva are "simple criminals", and federal law enforcement (which Starfleet inarguably is) go after groups like them.
Seven is downright boring this season, Shaw is far more interesting. Unless we get a surprise Janeway appearance and scenes with Seven and Janeway. But the actresses hate each other so I doubt it.