RE: do ailerons provide lift?
You are right to say that adding elevator increases the total lift vector. What I don't understand is your claim that doing this does not make the turn tighter. Since the plane is banked in a turn, the lift vector is not vertical. Therefore, increasing that vector increases "lift" in two directions: upward and in the direction you are turning. The extreme case would be if you are banked 90 degrees, in which case adding lift would only tighten the turn and wouldn't raise the nose at all (possible coupling aside). To be sure, we do not usually bank that much except when we're having lots of fun. But the principle is the same even in a 45 degree bank, where about half of the added lift tends to move the plane's nose in the direction in which it is turning.