In my experience, yes. The only difference is that you don't have a visual flame so it takes a little getting used to which setting means what (unless you have the type with a knob and a temperature readout, but I do not).

It depends on the stove. The gas stoves in my building are much better, but that is because this place is ancient and the electric cooktops in question are whatever crap they find secondhand.

Depends on the quality of the stove. The bad ones regulate like most resistive glass ceramic stoves in on/off pulses, which is fine for ceramic because the thermal capacity smoothes everything. I've got a mobile induction plate like that tho and it is absolutely horrible to work with.

My decent quality stove top goes from just hand warm (keep warm function) to the fires of mount doom (power function for boiling water) in 17 silky smooth steps. On top of the pulses there is some power regulation as well (you can hear the coil hum change depending on power).