How to get chickens from trading post to one of my empty pastures?
You have probably bought Chicken which are dead Chickens. To have them in the Pen you need to buy living Chickens from the Livestock merchant.
Your c) statement that the "Chickens" meat is being sold at the market confirms this theory.
A simple way to see if it is a live or dead chicken(s) is that the value of live chickens are 400-500 and chicken meat is worth 3.
See trade screenshot for living Chickens