No parking fees, but there are some limitations as to where they are allowed to drop off. For example, some resorts restrict entry to Disney employees and resort guests -- so at those resorts, the driver would have to drop you off at the main lobby or a designated dropoff area. I believe FW is one of those situations.
Also, at MK, the dropoff spot is TTC for Uber/Lyft, but the MinnieVans can go all the way to the bus dropoff. (The workaround is to enter the Contemporary as your destination and do the short walk to MK.)