Induction normally does PWM of the actual oscillator, no real power control is possible with the cheap self oscillating designs they normally use, and thus at low settings they implement pretty coarse PWM to get low average power, and also to avoid harmonics being impressed on the mains, so the drive has to be an integral number of full mains cycles, and thus the low PWM frequency. Hard to do single pulse control that way, better to have a longer time, say 10s total, and average over that.
Yes the single plate ones all are pretty much the same electronics inside, similar controls for power as well, and thus similar characteristics. Only a few power levels as well, some have more, some have less, but pretty much only a full stove will have any form of temperature feedback, simply because of the very poor coupling between the pot and the glass top, deliberate though it is, and also because your sensor wiring will also have massive common mode voltage in it. About the only feedback is detecting pot size on the built in types, using a few separate drivers, and sensing the open circuit voltage and current on them, so as to detect pot size, and presence on the top every cycle, so that the power can be turned off before it destroys the oscillators.