When making chicken stock, do you skim off the fat after its made and cooled in the fridge?

Like POLC I skim and keen

I do, but not too aggressively. Most molecules which carry flavor are fat-soluble. Whatever you go on and make with your stock will be much more flavorful if you leave a small amount of fat, as Garlic Friend also suggests.

I let it cool, lift off the fat, wrap it in plastic and keep it in the freezer. Its culinary currency!

Yes.

You can. For me it depends. If there's only a little fat, I don't skim. If I'm making the soup for someone who's under-nourished, I also don't skim. I do skim off the floaty brown stuff to make a clearer broth though.