Wouldn't the Crooked Man fight him if they try to protect David and attack the Crooked Man?
If they protect him yes, but I dunno how much sense of self-defense he has, game is generally pretty ambiguous regarding exactly what it is and how much self-agency it has.
Although, to answer the question, Lockwood might qualify to an extent. It's been suggested that his tendency to take great risks to some degree originates from a death wish he developed after his parents died in a car crash and his sister shortly after was killed by a ghost.
Yeah that might work, between the fact that there's more "proximity" and that, the Crooked Man might lock on to him instead.
They would get plenty of their equipment for a start, but I assume you mean mostly information wise. Tbh, I don't know the game enough to say. George would usually go through the death records and newspaper archives to dig up anything from the right time period that might be related. Assume David gives them whichever initial information he possesses, they would likely research the legend and whichever places David points them to be relevant. A floorplan of the latter should be something they can get in advance.
To tell the truth at the beginning of the game David doesn't really know of the Crooked Man or anything, he just
got some creepy messages and
an address, which leads him to the hotel, which is the first of the three "dungeons" of the game.
From there it depends a lot on how public the issue was.
To my knowledge not particularly, it's not actually top secret or anything but it's a dude with no friends hanging himself in his home, and seemingly not being discovered by the police at all. There's a diary of a doctor driven to suicide by the Crooked Man that you find in the hospital (third area), he's haunted other people before so it's possible that they might find other instances of that?
Whether they split up does vary on how large of an area they have to search and how active the Crooked Man is. They usually split up if they have to keep an eye on many rooms or search a large place. The exception is if the ghosts are very proactively hunting them (or if there are many ghosts). Then they might not do so for their own safety.
Going by the game, he takes a while to show up, in fact David is the one to bump into him at first. The first place of investigation is pretty big (a huge, two floor hotel) and they only get bigger so I think they might.
It should be noted that Lucy's and, to a lesser extend, George's and Holly's ability to hear ghosts comes in handy for locating him and evading surprise attacks.
I'm not sure if he qualifies as a ghost, considering he's material and more like an avatar of sorts coming from the corpse. How does this manifest?
Btw. what information is concerned, they can pick up visions of past events once they are at the haunted place. So even if their prep doesn't result in much they should eventually find what they need.
I mean the information is there anyway, David gathers it with ultimately no special abilities, this might help them get it faster though, or realize that the illusions the Crooked Man sends them (of past people in his life/his past self) are just that. Granted, Lockwood may be the only one to see them anyway, since they only appear to the one he's "locked on" to. Well I say "sends them", dunno if it's a strategic move or just something that happens.