In several states, an 18 year old can possess a handgun if furnished by a relative over 21, or if purchased privately within state. Federal law prohibits purchase, but not possession.
Gun shows are entirely legit, and all dealers run their purchases through NICS, as the law requires they do at any location.
A private citizen may sell a firearm to another private citizen, regardless of where they are (house, gun show, parking lot). Federal law prohibits "engaging in the business" of selling firearms. Occasional sales of personal property are not deemed "business," any more than a garage sale is considered to be a store.
If you are obviously antithetical to firearms and not comfortable with the subject, the scene will not be believable.
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One issue with smaller handguns is greater recoil. My pocket .380, with 40% the power of the loads in my 1911 .45, recoils harder, and my wife can't shoot it. She can easily handle the .45.
My 14 year old daughter can comfortably shoot .357 magnum out of a Ruger Security Six 4", but can't shoot the .45.
There's also an issue with cycling the slide to charge the weapon.
Smith and Wesson, Ruger and Taurus among others make compact revolvers for smaller hands. Grip material and shape also play a big part. Females often prefer round butt revolvers due to finger geometry.