do they carry any types of birds? (sun conures, cockatiels, or lovebirds) if they do, how much is the price?

No

Currently no in the springtime they carry chickens turkeys and ducks

No birds, only chicks and baby turkeys in the spring

No, it's not a pet store. As answered in previous replies, they have baby chicks, ducks and turkeys for the farm or where they're allowed, in the springtime.