When you have acute plantar fasciitis should you rest the foot elevated or down?

Your choice. Whatever makes you feel better. If you have been on it all day then its time to elevate and ice. If you have been asleep and get up then its time to stretch and heat it.....
No difference. Healing will occur regardless of whether it is elevated. The effect of elevation is more upon swelling than on healing. Excessive swelling is a different matter, but is not as common with plantar fasciitis.