know Mars has a Purugly, but the question here is how Skye
knew, when she had no prior information about the Team Galactic admins.
Something that kind of bugs me about your explanations, Strife89, is that you're not pointing out stuff that's already in the story, but just introducing a bunch of new information to explain things. You can't just leave plot holes in the story and only explain how they make sense when somebody asks. This stuff should be in the actual fic, one way or another - when there is no way the reader could deduce from the content of the story why event X happened or how character Y could do Z, any explanation you give as the author afterwards is going to feel like a half-assed excuse no matter how well you actually thought it out beforehand. If Skye has Lily's papers or whatever, then for God's sake mention
that somewhere. It would be very easy to fit this in, thanks to the fact that Brendan himself has every reason to wonder how she got that information.
Given the time, Skye is capable of fully analyzing a print on her own; Brendan remarked earlier about how the team wouldn't have "a result in time for the trial" without her. I guess it kinda feels almost Deus-ex-machina-ish. :/
.... Okay, I admit I came completely out of left field with that one. The only "explanation" I really have is that Skye made several deductions of her own, using hunches and details such as the date of finding the thing, Brendan's investigation (she gleaned information from his brain as he passed by, getting details such as the killer's appearance, etc.; and checking his evidence), and so on, then somehow (psychic computer operation?) running a check against that one person - and getting a match.
Again, this is information that should be in the story. The reader has no reason to assume psychics can remotely operate computers (watch out for that; one of the major problems with writing psychic characters is the danger of making them too omnipotent and having a hard time actually getting them into honest-to-God trouble without conveniently forgetting about some of the things they can do) or that she extracted information from Brendan's brain. If this is how she found out this stuff, have her actually tell him about it. For instance...
"Brendan, I've found something! I read the description of the criminal from your mind when you came here earlier and it rang a bell, so I checked the papers that I snagged from Lily again [wouldn't those be important evidence, though?]. See this page. It seems this Mars person has a Purugly - a cat Pokémon - and her fingerprints are in the file - they match the ones on the trinket! I bet it was her!"
Just a little snippet like that gets everything to make much more sense for the reader. This isn't obvious stuff, so it's not dumbing it down or otherwise annoying; it's just information that helps connect the dots and make sense of how the story is coming to develop the way it develops. I recommend you try to watch out for this and include more information about nonobvious things that are required to properly understand why things happen.
Normally they would use a block of some sort (but note that Mewtwo didn't leave his cell in ShadowKnux's fic, and they never say if there's a block or not), but an unmentioned detail is the fact that some of the police took pity on Skye, and are allowing her the leeway of the honor system (and she remarks that she can't exactly leave jail and help Brendan investigate solely because it would just make the situation worse); you could say that this is why she has such free reign with her powers (less scrupulous psychics would likely use their abilities to "trick" the police into legally setting them free, had they such free reign; so yeah, they'd use a Pokéball or knock 'em out).
Honestly, though, she's a murder suspect
. There is no way the local police department has any authority to give her this kind of leeway; they're blatantly endangering the citizens they're supposed to be protecting by setting a potential killer loose, for eff's sake. It doesn't matter that they like her and she used to be on the force. If I were the chief of police I'd fire everyone involved and have her transferred somewhere else if I heard about this. :/ Is there any particular reason not to just say they have, say, Dark-type guard Pokémon that use Mean Look and can't be affected by psychic powers? Is it actually important to the story that she can
teleport freely out of her cell if she chooses to? If it isn't, I strongly recommend you scrap that part because it's just so wildly implausible.