Well, I'm actually completely ignorant of Mandate history so I can't help you with the Zionism question, but I can say two things:
You need a POD before the Balfour declaration, since with it Britain assumed responsibility for creatinga Zionist state in Palestine.
Nazi and Vichy plans won't amount to anything because Vichy Palestine will get stomped on in a second. There would be no strategic reason for France to garrison the mandate anything more than police forces before the war, and by nature Palestine is a grave threat to the Suez canal. Syria, by comparison, was invaded over reports that the Axis might use it to bomb Iraqi oil supplies, hardly a threat of the same magnitude as a chunk of potentially hostile territory within a dash from the British Empire's jugular vein.