Dipped beam, yes - main beam, no.
NO
No, you should not.
Low beams - high beams only light up the snow or fog which further impairs vision.
No, you should not.
low beams
You should use low beams when driving in fog. It is more difficult to see driving with high beams in fog.
Use your low beams or fog lights. Fog or snow will reflect high beam light back in your eyes making it more difficult to see.
You should never use high beams when you are driving in fog because they shine up and ahead which will be reflected straight back into your eyes by the fog. Low beams (which aim downwards) and front fog lights (which are lower) are far better suited.
Yes
You should never put on your high beams - it makes it much worse.
Use the low beams if your car is not equipped with fog lights. It's never recommended to use high-beams in fog, as it makes it about 4x harder to see, and makes the fog look denser.
Driving in fog you should drive with you dipped beams. Putting full beams on will just deminish your vision. turn on your fog lights also, but dont forget to turn them back off again when you clear the fog.