they like little dens or small sheds with water, food, and fresh bedding
mostly goats lives in Farms but more specifically they lives in pens or byre.
Not if you have some trees but if it rains or snows the goats will prefer some sort of shelter to get out of inclement weather conditions.
By standing under trees or behind a shed.
By finding a dry spot
Food, water, air, shelter and veterinary treatment.
When winter comes around, mountain goats seek shelter in stands of hemlock or spruce. Mountain goats are found in several states including Alaska and South Dakota.
A shelter for goats can be a lean-to, a barn or even a paddock. The most common term to refer to a goat shelter is a "shed". It is usually a 3 sided building with a roof and a fence across the front and some contain small goat stalls and a milking stand.
Food, water, air, shelter and veterinary treatment.
Yes if they are provided with good food, water and shelter.
They may not feel comfortable or safe in there - put some edible straw in as bedding and they might go into their shelter.
You can probably take them to your veterinarian or animal shelter and they will care for it.
Mountain Goats are built for rough train so whatever they can find will do like caves, rocks, big trees, holes.