These are all good questions and I'll take them in order. Actually looking at Cabinet appointments, Balfour was Foreign Secretary for the whole Conference while Curzon deputised in London. Balfour was easygoing but essentially winged it as a minister; Curzon was pedantic and overworking, the total opposite. Bonar Law was less grandstanding than LG so I can see him taking Curzon to negotiate for a more consistent approach.
Very interesting, what is this going to mean in terms of altering policy?
Curzon saw British influence in the Middle East as protecting the route to British India; thus he was the only supporter of a long-term occupation of the Caucasus, so less knee-jerk anti-Turkism in exchange for building up the anti-Soviet buffer. Maybe dropping support for Armenia but keeping Azerbaijan independent.
What will he *do* differently based on that insight?
He took a special interest in Persia and wanted to develop British commercial interests there as a protectorate, but really failed to appreciate the new wave of nationalism after WW1, and took a very patrician view. So it would not end prettily if he tried to force his way in. Balfour was still be responsible for Palestine and at this time the Indian Office was responsible for Mesopotamia so if you have Edwin Montagu in post, you'll see similar policies for the time being.
According to his biographer David Gilmour, Curzon was the only senior politician to recognise favouring the Jews would antagonise the Arabs in the long run, so he might keep the peace better, as you say cut down on Jewish migration or concede Arab autonomy more. Other people like Herbert Samuel & Balfour would control other aspects, and this is key - for all his immense knowledge of the region, Curzon utterly lacked the people skills to bring his colleagues along. So if he intervened, it might make matters worse, but he could have some successes.
I don't know how he would handle the Hashemites - maybe keeping Jordan united with Palestine and creating a separate South Arabian kingdom. Curzon negotiated Egyptian "independence" in 1922 so that happens on schedule.
Isn't it a bit late for that with new nations breaking out and having formed themselves?
A very good point and I think by this point a more united Germany, maybe with the Sudetenland and Austria, the German/Polish border decided by plebiscites, is most likely, as part of a broader anti-Soviet front.
Curzon was far less romantic about seeing the White Russians as underdogs than Churchill, but hated Communism, so building a solid ring around Soviet Russia instead of directly intervening, is more likely. So a less strong "Hands off Russia" campaign overall.
Armenian independence can go either way, but certainly a much milder Treaty of Sevres, and if the Turks do go expansionist, none of the gung-ho approach Lloyd George took over Chanak.
Really, with a Conservative (one with Ulster Scots heritage at that) replacing a Welsh Liberal as top man in the coalition for three years, the British government won't be any more stubborn about accepting the Irish Free State as part of an Anglo-Irish Treaty in Dec 1921? And he wouldn't be any more stubborn in the face of Labour demands?
Up to a point - Bonar Law told Austen Chamberlain that he only really cared for Ulster, and the rest was fair game, which understandably annoyed Southern Unionists like Walter Long. Even Carson preferred a united Ireland with a Protestant minority, and only used the UVF etc to prevent Home Rule across all of Ireland. So you might see OTL but worse - Northern Ireland opted out, way more bloodshed down south, very likely no armistice of 1921.
As for labour demands, many strikes were a natural response to the economic downturn of '19-'21 but Lloyd George reacted with his typical heavy-handedness. In 1917 he said he saw a fight between him and Henderson for the political future, so he was motivated by fear throughout. Bonar Law had far more tact and humility, so was far less prone to reaction and grandstanding.