A non-Jew living in Israel and selling bread, is he supposed to take chalah?
And if not, is a Jew allowed to buy this bread that was baked in Israel without chalah taken?
Dough that was owned by the non- Jew at the time that it was kneaded has no requirement to have challah taken. A jew may buy this bread and he does not have to take off challah because at the time of the obligation it was exempt from challah. As a side point if the bread was baked by the gentile it would be pas akum, and a bigger issue is that bread nowadays often has numerous other ingredients added to it, (shortenings, and various chemical agents) therefore it would need a hechsher.
Shulchan Aruch Y:D 330-1.