I am working this line by line based on the hint at homonyms. I believe the final answer or target is probably an acrostic of sorts, or something common between all of the words. Not sure yet.
Although, another thought just occurred to me; perhaps the answer itself is a homonym set in which each word is four letters long, like:
Fawn like a young deer and fawn like a servile display of flattery.
I almost am a chicken,
Chicken like cowardly and chicken like the bird. Could also be hatch as in birth from an egg and hatch like a door.
Not quite a famous horse.
Could be stud like a board in a wall and stud like a stallion.
Confined to my domain,
Could be address like speak to a group and address like a place. Could also be yard like three feet and yard like a piece of ground adjoining a house.
I'll help you see the course.
Could be journey like traveling and journey like a long process of change. Could also be trip like traveling and trip like fall.
I almost am contagious,
Sick like, well sick; and sick like too much of, also sick like excellent (informal).
Not quite a Youtube part.
Could be watch like observe and watch like the timepiece.
Use a pencil when you're ready
Could be draw like make art and draw like draw like extract.
And light me when you fart.
Match like matchstick and match like a pair.