Does facilitated diffusion require energy? Why, or why not?

no it doesn't. it's called facilitated diffusion only because it's done through channels. this process is done due to concentration difference .from higher concentration to lower concentration. the only important feature is that the process is done for molecules that are very large or so polar that they can't p through the membrane by simple diffusion so they are transported through protein channels. and there is no need to energy because the transport is in concentration direction.