They were, but with a majority-Greek population. They are unlikely to go to Turkey if Greece is allied. Your post is a good way to get an allied Turkey, but we still need Greece to go Axis- possibly a disagreement with Turkey, but this may not be enough. With Metaxas, though, it may be.
Yes and no. If, at the conclusion of the fighting in Europe, Turkey occupies the Dodecanese and isn't interested in leaving, there is some potential for them staying. While the islands were mainly Greek, they hadn't been held by Greece since its independence, iirc, which makes them fair game for a transfer. Turkey's friendly relationship with the USSR leaves them with a potential backer here, as the USSR could support Turkey's claims in exchange for Turkish support for Soviet control, direct or indirect, over northern Iran or parts thereof. Soviet support would go a long way towards stopping the Western Allies forcing Turkey out, and threats of Soviet support for the Greek Communists could quell Allied support for the Greeks. Greece isn't really in a position to be demanding anything postwar, given that they have a civil war to fight. This would entail a Turkey which is fairly Soviet-aligned, though, but that isn't totally out of the question - I could see a Finlandised Turkey here, rather than another Soviet puppet.
I cannot see Fascist Italy and Metaxas's Greece on the same side in any war, to be honest. If both sign on to the Pact of Steel then Germany will have its work cut out for it trying to keep them apart. Italy made no bones about their territorial and political ambitions towards Greece pre-war, and the Greeks were well aware of this. A part of the reasoning behind the Greek leaning towards the Nazis was the idea of using Germany as a counterbalance to the Italians - Germany and Italy didn't really get along too well until the mid-late 30s. A neutral Italy is possible - just have Mussolini not get involved during the Battle of France - but that may butterfly away the significance of the Balkans, with both Yugoslavia and Greece remaining officially neutral but pro-German. An Allied Italy is possible with a POD in the early 30s, but the butterflies would be very significant again.