There is a clue here, "the heat sink side", it is designed to be clamped onto a heat sink in order to get the maximum rating out of it. To get the maximum rated value you have to have what is called an "infinite" heat sink. In practice this means a heat sink so big ( or force air / liquid cooled ) that it doesn't rise in temperature above the ambient. This is the sort of "trick" that the marketing department play to get a good headline figure. They do it with all sorts of components FETs in particular.
No, the point about using a single SCR is that it can only run at 50%.
Yes, while in principal phase angle correction is simple, in practice the value and characteristics of the capacitor involved are complex to calculate. All heavy users of electricity (industrial) have a meter that measures phase angle. It used to be on a pen recorder but no doubt they have better ways these days. If the phase angle went above a limit even for a few seconds all the electricity in that quarter was charged at a much higher tariff. This provided an industrial user to invest in an automatic phase angle correction system. These were big systems, about the size of a large garden shed and banks of capacitors were switched in and out depending on the current load of the factory and phase angle at any one time.
I think the domestic ovens work on the normal bimetallic thermostat method clicking in and out certain temperatures.