Yes there is a fee based on space size. Check out their website. I have never heard of a farmer's market not charging vendors for their space.
Yes. You can go here for application. http://takomaparkmarket.com/become-a-vendor/
I have only been there as a consumer not a vendor. It would be worth a visit and ask one of the vendors. They are all nice people and I am sure they will answer your questions.
Thanks! Your answer is awaiting moderation.