A proper 120v circuit has a hot, neutral, and a ground. What you describe is a hot and a ground. While such an arrangement will function it's certainly not to code and potentially dangerous. As suggested your best bet is to run a new 20-amp circuit. The other alternative and I'm not sure if current code allows this is to remove the existing 50 amp, double pole breaker and replace it with a 20 amp, single pole breaker. Use one of the two insulated wires in the existing cable as your hot and the other as the neutral. The uninsulated wire is the ground. The problem is that the heavier wire typically won't fit in a 20 amp breaker or receptacle. So you need to connect a short length of 12 ga. wire at each end of the two heavy wires, most likely with a split bolt. I'm sure someone will comment on if such a method meets current code.

Just don't do it with Jenn-Air appliances. I was going to do the exact same thing (36 inch gas cooktop and 30 inch electric oven) until I plugged in the oven and it was very loud. The oven vented out the front and a very loud blower made it sound like a microwave vent was on (nearly the whole time the oven was on bake). The look you wish to accomplish is very clean and custom. I too, had ordered pannels for the sides and it would have made for a very clean, sleak look. It was just not to be for me. I purchased a 40 inch range instead and am pleased with the purchase. I am a DIY and the cooktop/oven option would have taken considerably more time. Do the 30 inch oven and 36 cooktop, it will look great!

In Europe, buying a separate cooktop and wall oven is a very common configuration. So, if you are in that market, I wouldn't hesitate. But in the US, manufacturers don't really plan for this particular configuration. Wall ovens often are too tall, resulting in the door being too close to the floor and the top of the appliances hitting the cooktop. I'd strongly discourage you from going this route. If you do want a cooktop, then put the wall oven at roughly countertop height into one of your cabinets. It'll work much better that way. If you prefer a cooktop, get induction. I would never recommend cooktops for gas; it's just not as functional. Instead, with gas I'd get a rangetop (i.e. controls are on the front face of the cabinet). Bluestar makes a wonderful gas rangetop, by the way. If you do consider Bluestar, do not get the closed burner model. It's not playing to this brand's strength. We occasionally have this discussion on Houzz, and inevitably most people regret their decision, if they don't heed our advice. I strongly discourage you from buying a hood based on looks, only. While a hood looks like a very simple appliance, it is actually one of the more difficult things to get right. You'll regret your decision if you end up with something that looks good, but that is otherwise just noisy and doesn't actually vent. I probably would buy from a reputable vendor such as ModernAire or VentAHood, rather than from a general-purpose vendor. Miele makes great appliances in general, but vent hoods are really not their specialty. I am not even sure they make their own rather than rebranding somebody else's product.

AJ Madison has 18 radiant/smoothtop (not induction) 36", stainless steel ranges for less than $3000. Frankly, you are better off with a 30" range as there are many radiant/smoothtop and induction for less than $3000. Thirty-inch is the standard size and the market in which manufacturers compete fiercely in price, quality, and features. AJ Madison has 108 radiant and induction 30", stainless steel ranges.