How to get livestock in Banished

Crop fields will, on occasion, pull nearby workers to help harvest their yield. This is because designated farmers will turn the crop into food baskets and, on occasion, leave them to go do something else (bring food/firewood back their house, go to sleep, etc.) At this point, the food basket becomes a resource just laying around and any nearby citizen will pick it up and take it to the relevant storage facility. Said resource will now count as being produced by the citizen's work facility, leading to your fishing docks producing corn and (in my case) mines producing wheat.

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