A pro tip for stopping your windows fogging up, don’t use aircon. Most of the fog is trace refrigerant in the system being blown onto the glass. Turn your aircon off and clean your windows thoroughly and they will fog up much less and not need cleaning as often. During those couple of days in the summer when aircon is actually needed, set it to feet and forward vents and not the screen. After use keep it off the screen for a good while to allow any gas to clear the system. Had my current car 3 years and 1 month, used aircon 2 or 3 times and cleaned my windows maybe every 3 months.
Air conditioning actually helps to reduce fogging, as it dehumidifies the interior of the car – just adjust the temperature accordingly for the time of year. I run my AC in my car almost permanently; in summer it keeps me cool, in winter it keeps me warm, without fogging up or me needing to ‘crack a window’. Trace refrigerant has nothing to do with it (shouldn’t be leaking anyway) and it is only cold when it is in the system anyway.
The only downside to air conditioning is that it draws power, therefore stealing some from the engine and also using marginally more fuel. For me, it’s a trade-off that I am comfortable with.
OP – my heated windscreen goes off automatically after around 1-2 minutes in my car, and this is normal. The idea is that it clears the screener from ice/frosting/whatever, but you then adjust your heater in the car to keep the windscreen clear (and I’d recommend trying having your air conditioning activated, but the temperature set higher, perhaps around 21-22 degrees). Just keep it on a low fan setting, but set to blow onto the windscreen.