Who killed Alex's cousin?

I don't think we can know.
But what do you think? She didn't seem to be trying to protest her innocence.

The question for me is why did she kill him?

There are a few narrative clues that seem to point to Bojan (Alex's cousin) being killed by his own wife. First we see her in the background staring at Bojan with his hand on Kate's knee. This was done minutes after the script went out of its way to make sure we knew that was indeed Bojan's wife. Next, when Kate is trying to seduce Alex later that night, she is very demure and evasive about her own current sex life. Given the size of the village, her mystery man is probably someone we've already seen, and Bojan seems to be the best candidate.

Later, shortly before Bojan is found killed, his wife is clearly looking for him. There is probably more corroborative evidence in the first part during the funeral scene, but I did not go back and specifically look.

Finally, as to why they suspected the girl? That's what the movie is about, right? Being in the wrong place at the wrong time, and that this kind of violence will find you there even if it isn't looking for you, or you for it. She and her brother probably came searching for a better view of Alex, and they happened to be seen around the paddock when Bojan was killed. The Macedonians (or the Albanians if the situation were reversed) didn't need any better reason than that.