For the 2013 you would need the 12x23 cut style flaps for the front wheels. There is no bracket needed for the front wheel wells. On the rear the 12x23 full style flaps and the bracket needed would be GB755006. This will give you a good stable mounting surface for the rear flap.
Yes, you can buy only the rubber flaps.
Here would be the rear flaps for the F-150 - https://www.sharptruck.com/truck-hardware-gb1223bk
here are the rear flaps for the new Super duty SRW - https://www.sharptruck.com/truck-hardware-gb1226bk
Here is what you would need for the 2001. The front flaps do not need brackets and will install with self tapping screws to the lip of the fender.
Front Flaps: https://www.sharptruck.com/truck-hardware-gb1223cutf-c
Rear Flaps: https://www.sharptruck.com/truck-hardware-gatorback-mud-flaps-blue-ford-oval-19x24-dually-gb1924f-c
Rear brackets: https://www.sharptruck.com/truck-hardware-universal-fit-mounting-brackets-gb758054
The plates are sold individually. You can find the Ford licensed plates here, https://www.sharptruck.com/truck-hardware-gatorback-ford-replacement-plate
Here is the set you need for the truck, https://www.sharptruck.com/truck-hardware-ford-f-150-blue-oval-gatorback-mud-flap-set-gb1223cutf-c-gb1223f-c-gb759524-gb759543