No, FAA doesn't own the rights to your art, you do. They do not take a commission on originals. Yes, you can sell just originals but you will prob be back in the search since you're not selling prints of your paintings. People contact you directly if they want to buy a painting, FAA does not deal with the originals at all, it's totally your responsibility.
Upload your art. Fill out the box for originals, then delete the prices that show up for prints or don't put any prices in the boxes - nothing will show unless you put a price in the box for prints, cards or phones. So just leave the prices blank except for the original. You can explain about the painting in the description and you might want to activate the preview since you're selling the original so people can look at it up close. You might want to make galleries for your paintings if there are different subjects. Hope this helps -