D&D 5E Play out this scene

[Unwise]

I skimmed the topic, then did not read the description of the place/situation at all, so that I could give an authentic player/PC reaction.

Druid: Ok, so its just one guy we have to kill? I rolled a 19 for initiative. Where am I on the battlemap?
Rogue: What the hell are you talking about? Kill who? What battlemap? Why are you rolling initiative?
Wizard: I cast Mage Armour before we get into combat? I think I said that earlier, or I meant to. Can I do that before I roll initiative?
Rogue: Why is everybody rolling initiative?! We are here to...
Druid: I'm getting a beer, let me know when it's my initiative. I cast shield if anything attacks me before my turn.
Rogue: What would attack you? Why...how are you even casting shield? You are a druid.
DM: ...actually I think I'm going to need a beer too while you are at it...

 

[Swarmkeeper]

Assuming it's dark
Wizard - casts the light cantrip. "Can't very well find evidence in the dark".

Rogue - checks for traps, especially focused around the oval rug and desk drawers. Ultimately carefully rolling up the oval rug to check underneath. "If I was going to commit the kind of indiscretions he's accused of I wouldn't very well leave evidence alone in an untrapped room".

Druid - Shapechanges into a cat while heading back outside. "I'll be the lookout".

Cool.
Now how would you, as DM, adjudicate these action declarations?

 

[Swarmkeeper]

If we are supposed to be looking for malfeasance on the merchant's part, I would want to look over the "shallow box of paperwork," as well as look for any hidden/secondary paperwork to compare with. Any false payments records/invoices? Any cooking of the books? Any blackmail letters or payments sent/received? Any indications of illegal materials shipping and/or smuggling?

Sounds good. How would you as DM respond to this particular aspect of the investigation?

 

[FrogReaver]

Cool.
Now how would you, as DM, adjudicate these action declarations?

Light just works. Wild shape just works.

the rest depends on how I’ve preset up the room and on whether anyone of note has been predetermined to approach.

 

[Rabulias]

Sounds good. How would you as DM respond to this particular aspect of the investigation?

As a DM, I tend to overplan, and provide more background info and detail than ever comes up in the game. So for this case, I would have already prepped a bunch of info they could find depending on What Is Really Going On, including some possible red herring clues that might mislead players if they don't think things through. IMO, investigations in play do not work very well unless the DM has a good idea of how/when/why/where/what is being done and by who. As players work to uncover the mystery, the DM needs to have answers that logically fit together. If they just pull the answers out of a hat, then it will not make sense, and the players have no fair chance to figure things out. Players will take up lines of thought and questions the DM did not consider beforehand; the best way to be ready for them is to have the whole picture ahead of time. Little details and side things can be added/improvised during game, of course - that's part of the fun - but the main throughline of the events needs to be solid. On top of this, players may sometimes miss leads and clues, so the DM needs to have redundant ways to discover the same piece of info.

In this particular case, I would like a convoluted plot where someone is framing the merchant in the eyes of the Captain of the Guard, with the ultimate goal of pushing the captain to violate the law/their oath by punishing/killing/sending adventurers(?) after the merchant. When the merchant is revealed as innocent, the captain will be disgraced and have to resign, or worse, be tried for crimes. Who is behind all this? A crimelord imprisoned by the captain, but still able to exert power outside through minions (think Kingpin from the Daredevil TV show)? Or maybe the merchant guild member spouse of the captain's secret lover? Or the parent of a city guard slain in the line of duty who blames the captain for the loss of their child?