(CONTAINS VAGUE SPOILERS FOR DOCTOR WHO)
The Agents
I have some concerns here regarding both characters. First off, and perhaps most notable, is the Detective. Describing one of your protagonists as 'an irredeemable jerk' is something of an issue. 'Irredeemable' means that there is nothing about this individual of merit, nothing that makes them a likable person. What's more, it means they never will gain any sort of positive trait. So why follow them? Even villainous protagonists typically have something that endears them to the audience, such as intelligence, honor, charisma, etc. Jerks… aren't really interesting. Well, unless they get comeuppance, which seems to be something that occurs in at least one of your prompts. But as it stands, the prompt just makes him seem like someone who would be unlikeable and get away with it.
My concern with Jack Riggs is less to do with with characterization—stout, stalwart characters are nice to see and have a lot of potentiality, and having him be unconvinced he isn't still in an illusion is something that could have a lot of play story-wise—and more to do with a canonical issue. You say he joined the PPC at age 19, and is now somewhere in his 30s. The issue there is that Supernatural first aired in Sept. 2005. That means, at oldest, he could be exactly 30. Having him be any older that would make him predate his own universe of origin. This is an easy thing to fix, though.
I... also must confess as to not being all that excited to see a new Time Lord agent. Or a new pair of Floater agents.
The Prompts
Regarding the first prompt, I admit to starting out very confused. Why was DoSAT after Jack's heirloom journal? I don't ever recall DoSAT seizing the personal possessions of agents before. Sure, it makes more sense that they would be concerned about a TARDIS, but that just made me ask: why don't they use the TARDIS as a response center? I'm also confused as to when this is taking place canonically. I was under the impression that Gallifrey was back (sorta, kinda). So… why is the Detective doing all this, then? Is this taking place in the past? Does he not know?
All that said, the first prompt is otherwise fairly sound. The characters banter well and the prompt is integrated well. It's a good piece, despite the questions that nagged at me.
The mission received story is also very solid, but lacking in some areas. Some of your sentences tend to drag on to such an extent that they become awkward to read. The first sentence of the second paragraph, for example, as well as the eighth paragraph in its entirety. You use commas when you really don't need to.
Some continuity errors: the Detective corrected himself, saying he was late by five hours, then said he walked in an hour after the Marquis de Sod told him. Should it be five hours? Also, the Marquis de Sod has nothing to do with assigning missions. If these are Floaters, then it should be the Floating Hyacinth whom he annoyed. Sure, the Marquis could have pulled in a favor, but that doesn't explain why Jack immediately thought of him instead of his own boss.
SPaG note:
—Missing quotation mark on the second page of the first prompt, (Before 'Considering.')
The Badfic
Wow, that looks like a mess of a crossover. And Harry Potter is apparently a god? Yep, I'd say this qualifies.
You, as a Member of the Community
No problems here. You participate on the Board, you're a regular in chat, and you play a mean game of Cards Against Humanity. You can work with others without issue. I have no concerns as to how well you would fit in.
Verdict
I'm going to have to say Permission Denied… but barely. Your writing is good, but there a few issues here and there that got underneath my skin. My biggest concern is with your characters. I feel like you should spend a little bit more time tightening them up.
It was a very close decision on my part. And I'm pretty darn confident that you'll nail it next time. But for right now? You should take another look.
PC