Those two guys, Tarumi and Hanamura, are definitely forgers based on the bathroom conversation. Hanamura cut his thumb, presumably setting up a trap for the item(s) from the exhibit that they're going to steal. Kid is almost certainly planning to expose the items in the new exhibit and the old items stolen by the lady thief he is returning as frauds. This is definitely going to be a four part or more case since Conan will need to work out the details behind the other forger's heist as well as kid's entrance.
As for what Kid was talking about by "lead from the inside grip" and "numbers are only numbers, what I was carrying was only a skeleton", I'm pretty sure he means he is smuggling the weapon in as parts.
Smith & Wesson 1 1/2s can be extensively disassembled as seen in the picture of this book a few pages down. The serial number of the gun is printed on the wooden grips (probably the number part kid had referred to just now) as well as the butt of the gun on the grip strap/butt strap (which is probably what Kaito is referring to by lead from the inside grip). There is also an assembly mark printed on various places as well.
As for how he got the metal components through, suitably disassembled, the pieces of the gun are rather small. There are two strategies for bringing the gun through that I can think of for now. The simplest concept would be to smuggle through all the non-metal components, then visit the bathroom. The window behind the bars had already been manipulated to allow it to open. Left in the window is a thin, near-invisible fishing line with nothing on it that hangs outside the window. Regardless of whether the window is on the ground floor or the second floor, Kaito Kid or an accomplice could have tied a camouflaged bag with the metal parts in it then pulled it up from inside the bathroom when it was clear. The bars are wide enough to allow the passage of the disassembled gun components. Kaito Kid could have been relying on the rain to obscure the raising bag. This idea of course runs into problems if the people nearby don't clear out, and since it's busy the possibility is likely.
The second plan involves going straight through the metal detectors. Since the police were looking for intact guns, perhaps he disguised the components in something innocuous containing metal - like an umbrella? The curved gun grip can be disguised as the handle, the barrel as part of the umbrella shaft, and the chamber and other small parts can somehow be incorporated into the design. He may hope the bag checker whose search image is an assembled pistol wouldn't notice the off parts of the umbrella.
The only problem with this theory is if he intended to smuggle the parts through in an umbrella with rain as has cover, it seems to me he that before he sent his second heist notice, Kaito Kid anticipated that he would have to beat metal detectors. The metal detector plan was set up after the second note and was prompted by Conan's idea. Kaito Kid couldn't have made certain that metal detectors would be installed unless he planned to influence the conversation by disguising as someone present.
Whatever technique he used to get the metal bits through, we will probably get more hints about it in the next chapter.
I wonder how the writing transferred to Sonoko's sleeve? Wet paint doesn't make much sense, but perhaps it's something that rubs or peels off when moist. I presume it has something to do with why Kaito Kid needed it to rain. Maybe as the crowd surge increases when the people cram in, they will bump up against the display cases with their wet clothes, removing the moisture sensitive outer layer of the display labels and revealing some Kid created message underneath about the stuff in the exhibit being fraudulent.
As for Kaito Kid's escape, maybe he could use the gun to shoot out the sprinkler heads and escape in the resulting mayhem.
In any case it might be hard to distinguish between the tricks the forgers plan to use and the tricks Kid used until we get more clues.
Finally as for who kid is, my bet is on Sonoko for now, but I have no evidence.