I am pretty sure that Kang beat Shinnok. He is the champ also the main good guy that can pretty much beat anyone in the MK world. While I don't have the 100% answer I think you can find the answer in MK: DA's Konquest mode, with Quan Chi. It was either that or Quan Chi killed him. Again I think MK: DA's Konquest connects the events to MK4 to MK: DA. Also I think one of the sticky threads above made by {ombat has a link where someone type out all the Konquest text of all the charaters. I am falrly sure that Quan Chi killed him, but the same time I think Kang beat him.

Kang can't beat everyone in the MK world. I believe raiden beat Shinnok.

I'm pretty sure Kang won MK4. In MK:D they have "Kang's Tomb" as a background, and if you read about it in the content part of the game it says that the 4 dragon symbols above the flame show his 4 Mortal Kombat victories. So yeah, he won MK4 as well.