Hats are worn all the time as fashion accesories, however they are most often worn in winter and in colder regions.
It is called "Yom mum" and sometimes a Pointy but is also reffered to as a Witching Bonnet even though it does not look like the other bonnets of its era.
In mines and at construction sites. In a wider sense, the answer might be 'on people's heads'. This is probably true in most places.
Water after a long time can break up rock.The main things that erode things are water,ice, sand,and wind. Hope this helps. :).I'm a science freak.
Kippah, however this is not specific to Rabbis. All Jewish men (and some Jewish women in modern congregations) wear a kippah.