Could the two sentences be separated by a comma as well: "Я не питаю чому, я питаю як."?
In Ukrainian, yes. In English, that would probably be classified as a comma splice and considered incorrect.
In English, you could also separate the two with a semi-colon to make a single sentence, although it's a bit literary: "I am not asking why; I'm asking how." Just in case anyone is interested. :) But that's right, the comma splice really isn't correct in English.
As for comma splices for longer sentences, it seems to me that that they are usually OK in Ukrainian, whereas the same sentence translated into English normally would not be OK. But I am not a native Ukrainian speaker, and I am relying more on my knowldege of Russian grammar. So I defer to others for a final verdict. :-)