Is it ok to put an electric heater (radiator) and its electric outlet in the bathroom, if yes what are the minimum distances from the shower and wash sink that are required?
Article 424 does not prohibit fixed electric space heating equipment from being installed in a bathroom, and my interpretation of 424.12(B) would not apply to the area outside of the footprint or the shower or bathtub. The potential temporary presence of wetness or dampness would not make the bathroom a damp or wet location.
The wet and damp location requirements can actually be found in  410.10(D) even though it doesn't come right out and say "heater." A normal luminaire would not be allowed anywhere in that zone. Only a luminaire that is marked for damp or wet location is allowed. So it stands to reason that the heater should not be located in that zone.
If it is a baseboard heater, you are fine. In fact it's done all the time.
If it is some other type of heater that is below, "the top of the bathtub rim," you are fine.
Anything else would be up to the local AHJ to interpret.
The receptacle must be GFCI protected.
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