I think it is probably because when something is "in the sun", it is in the light from the sun - the sunlight. Even though the sun is incredibly far away, we are experiencing the effects of the sun's rays. So in a way, we are also "in" the sun. :)

It's just an expression that we use. The sun might be a shortened form of "sunlight" - which might make more sense. "In the sun" would refer to being in the areas directly affected by sunlight - just like how people say "in the rain". A lot of people also say "under the sun" but I don't hear "under the rain".

Standing "in the sun" is a shortened way to say "in the sunshine" or "Standing in a place where the sun is shining". The opposite would be to "stand "in the shade". or "stand in a place where there is shade." Hope this helps

Outside with the sun shining, you are either in the shade or in the sun ( as in sunny part).