100k BTU sounds like overkill for a single burner unless your wok is HUUUUGE (like, fit to serve a large restaurant). I think that's related to your excessive carbon buildup. A little burned-on crap is normal, but that amount is a sign you're either putting in too much heat, or not keeping enough food moving around in it.
Carbon is... well it rhymes with "witch"... to remove. I've not seen it soluble in anything available outside a chem lab, and there are no easy tricks. Here are the removal methods I've seen:
Scrape it off. This is the standard for serious built-up carbon on pans (particularly ones used as smokers). Use a paint scraper or bench scraper, and steel wool. There are specialty tools for cleaning flat grills which have a flat, very sharp edge that work even better, but in a pinch even a stiff spatula will work. Yes, it's exhausting but it turns out to be surprisingly fast if you can pick a good scraping tool.
Burn it off, using the powerful burner or the self-cleaning cycle on an oven. Be prepared for a lot of smoke. Naturally, you'll have to re-season your wok, but this will remove some of the carbon.
I've HEARD people say they can get carbon off by repeatedly heat-shocking it. This means heating it as hot as possible and then dropping it into ice water. However, they talked about like 30 cycles, and it could render metal more brittle. Might be worth a shot?
Personally I'd either scrape the bejeezus out of it, or just ignore it.
Check the bottom of the pan; often useful information is stamped there. Like the brand, sometimes even model number. Assuming nothing useful:
Steel and iron are ferromagnetic. That is to say, a magnet will stick to them. Both are unlikely to be Teflon-coated (edit: though Wikipedia informs me they exist). The black (which is hopefully somewhat shiny) is seasoning (cooked on oil). Iron would probably mean cast iron, and would generally be heavy (my cast iron wok weighs in at well over 10lbs). So, if they magnet sticks, you probably have steel.
Some stainless steels are ferromagnetic, but most aren't. Stainless is also unlikely to Teflon-coated. But it'll probably be shiny, at least on the outside. So, if not magnetic, its probably aluminum. Aluminum is probably coated.
Teflon isn't the only coating that may be used. It could be anodized aluminum as well (which, I guess, may not technically be a coating). Or one of the newer nonstick coatings. They all look different: Teflon is very dark gray to black, anodized is light gray to dark gray. The newer ones unfortunately are numerous and some can be any color. (Your description of the color sounds like Teflon to me).
You could also try cooking a scrambled egg in it; start it in a cold pan. Teflon in at all good shape will release the egg very easily. Seasoning will, unless very good, probably have you cursing.
Best Answer
I have a similar wok, I bought at Target. It was described as "seasoned". I thought I was buying a genuinely seasoned wok.
Nope. It was a black coating just like the one you linked to.
It's a non-stick coating. It worked well for a few meals, then it started to peel.
I used a plastic scrubby to clean the sauce that stuck to the pan, and it cut through the coating. From now on, I will not buy anything from Target. Lie to me one, and you are done.
I paid $80 for it a few years ago. $80 would buy a genuinely seasoned wok back then.