What ring height does a 56 mm objective need on a 30 mm tube?

Roughly 1.31 to 1.39 inches from the rail to the centre of the tube, which usually means extra high, x high in most catalogues. The range exists because the objective bell outside diameter is not published, and the bell is what contacts the barrel rather than the lens.

There is no standard, which is the single most confusing thing about this subject. Most American makers publish to the centre of the ring and that is the convention used throughout this site. Some publish to the bottom of the ring instead, which produces a number roughly half a tube diameter smaller for the same physical part. Always check which the maker means.

Only slightly, and not for the reason people assume. The tube diameter does not change the objective bell, so the clearance requirement is the same. What changes is that ring height is measured to the tube centre, so a larger tube sits with its centre higher for the same ring. In practice the objective, not the tube, decides the height.

The objective bell touches the barrel, which is obvious, or it nearly touches, which is worse. A bell resting on the barrel transmits recoil and vibration directly into the scope, and a bell that clears by a few thousandths will contact the moment anything bends. If you cannot pass a folded note under it, go up a height.

Your cheek comes off the stock, head position stops being repeatable, and groups open up vertically in a way that looks like an ammunition problem. A higher mount also increases sight height over bore, which steepens the near part of the trajectory and moves your near zero further out.

Not deliberately. Matched rings hold the tube in a straight line, and different heights bend it, which stresses the erector and can shift your zero unpredictably. If you want deliberate cant to gain elevation, use a canted base or an insert system designed for it rather than mismatched rings.