1) Back when they were in production (1968-84), would it have been possible to produce a conversion kit to allow an HK4 to fire 9x18mm ammunition?
This may be a yes or no kinda answer.
On the “No” side:
I suspect not, at least not as the pistol was originally conceived. The “4” of the HK4 designation meant that the pistol could be converted readily to any of 4 calibers, from .22 LR to .25 ACP to .32 ACP to .380 ACP, simply by swapping magazines, barrels, and the attendant recoil springs wound around those barrels. If it had been possible to fit yet another caliber in there, HK would have called the pistol the HK5, instead.
That design criteria in mind, I suspect that the operating pressures of the 9x18 were too high to fit a barrel of sufficient strength (and consequent diameter) into the slide. The 9x17 operates at a maximum pressure of about 21,500 psi, while the 9x18 operates at about 24,100. Building a pistol to accommodate that extra 2,600psi may have put it beyond the intended size and role specifications. Additionally, the extra 1mm case length may have been a factor, too, if the maximum case length differences (0.68 for .380 and .713 for 9x18) meant having to cut an ejection port wide enough that the change in slide mass created timing or other reliability problems. (Interestingly enough, the maximum overall cartridge length of the .380 and the 9x18 are the same, at least according to Speer, so fitting rounds into the grip would not have been a problem.)
On the “Yes” side:
If the kit completely replaced the upper and could be made to fit the lower receiver, sure, I don't see why it couldn't work.
2. In that same period, assuming someone had the idea and resources, is there any practical reason why a J-frame version of the Medusa revolver couldn't have been produced?
Don't see why not. If sufficient resources are available, “practicality” is rarely a consideration. Both are capable of firing .357 Magnum and smaller ammunition, and the operational heart of the design is largely in the cylinder and extractor, which at first glance looks like pretty normal cylinder lockup.
3. Does anyone out there have any solid information on when and how Paris Theodore's original ASP pistol was marketed? I've only been able to find sketchy information on it that sort of implies that availibility was sharply limited and the weapon was introduced in the 60s or 70s.
Nope. Sorry. But there's a little information about it here
http://world.guns.ru/handguns/hg147-e.htm
which states that from 1982 to 1983 only about 250 to 300 of them were sold on the American market by Armament Systems and Procedures company. In its original trim, though, the pistol wasn't marketed but rather developed specifically for use by those in clandestine services.
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