does household wiring emit an electric field ?

The first answerer is referring to propagating electro-magnetic (EM) fields which form the waves of the EM Spectrum, from very low frequencies including mains electricity, through radio waves, microwaves, infra-red radiation, visible light, ultra-violet radiation and on up to high-energy x-rays and gamma rays and beyond.

However, I think you are referring to the static electric field which exists whenever there is a separation of electric charges, thus creating an electric potential difference measured in Volts. This exists independently of the magnetic field which is produced by moving electric charges, also known as electric current measured in Amps.

So the answer is that if there is an electric potential difference between any two surfaces, then an electric field exists in the insulating material in between, such as air. The electric field strength is proportional to the voltage, and inversely proportional to the distance between the surfaces. The SI unit of electric field strength is Volts per meter (V/m) which is also equivalent to Newtons of force per Coulomb of charge (N/C)

However there would be few places around the home where we would be "between" two such surfaces, as mostly they would be inside electric appliances, between the contacts of electric switches etc. An exception might be in the vicinity of a mains lead-in cable with undergound earthed pipework or an earth "mat" beneath us, or perhaps inside an opened metal distribution cabinet etc. Another exception would be if our house floor contains earthed steel reinforced concrete then there could be electric fields between the floor and all the house wiring. (But not so much with underfloor heating cables, although the "neutral" end of such cables when switched on could produce a field to the household wiring.

But no, it doesn't "radiate" into open space like a travelling EM wave radiates.

BTW, 60 Hz EM radiation is very inefficient and doesn't get very far. The frequency needs to get above 100kHz before significant power and energy can be radiated by EM waves. However, if we are exposed to 60Hz for significant periods and are very close to the source, then it could be harmful in the long term e.g. if our house is very close to a high voltage transmission line.

Electric current and electric magnet fields are always present together. The higher the voltage the greater the magnetic field.

Take a portable radio and switch it to a AM station and wave it in front of your electrical outlet. You will hear the 60 Hz hum. Drive under a mains power line with the AM radio on and you can hear the hum. That gives you a general idea of the strength of the field.

Yes, but so do people.

Nothing too serious.