Ling Ling Potsticker Sauce or Similar
I haven't had that specific sauce before, but I've had similar sauces (FYI, if you want to buy the sauce without buying the potstickers, you can buy them in small bottles in Asian food stores).

I don't know the exact ratios, but you can always start with a ratio of 1:1:1 of soy sauce (Kikkoman would do just fine here), rice vinegar (not shaoxing, that's a wine and not a vinegar; I would recommend Chinkiang/Zhenjiang black rice vinegar, but any rice vinegar should do fine), and sugar. Start from there, and adjust as you see fit. You may want to dilute it also; I just made it and it tasted quite strong to me, may want a bit more sugar than 1:1:1.

I would skip the cottonseed oil and just use sesame seed oil - a few drops of good quality sesame seed oil (Kadoya brand, for example) is good enough. Chili oil/sauce - that depends, even Sriracha would work well if you like that flavor; a few drops of that would do.

Have you thought about possibly using a bit of chopped garlic/garlic powder? I've seen it in some of the ingredient lists of the bottled dipping sauces. Just a minor thought if you happen to like garlic - it's perfectly fine to use some in dipping.

Hope that helps!