In my experience, these two uses are not interchangeable.
The transitive verb "feed" means to provide food to someone/something. Your first and third sentences are examples. The subject is the provider.
The intransitive use of feed (as would be exemplified by "feed on") means "to be sustained by" or "nourished by" something. The subject is the eater.
Jane fed the children macaroni and cheese.
The farmer fed oats to his horses.
Buzzards feed on carrion and roadkill.
Sharks feed on fish and other sea creatures.
For your last, I would say "I feed my chickens corn".