350 ft. of 14/2 and 150 ft. of 14/2 That's what the original post says. 20 amps.
14 awg doesn't belong on a 20 amp circuit, certainly not 350 feet of it to a 800 watt load and another 150 feet of it to 300 watts in the circuit!
I doubt that 18 awg lamp cord is for 800 watts of lighting or is more than 6 feet long.
Extension cords aren't legs.
Since when do we assume 14-2 is extension cord?
Since when do we consider an extension cord, portable lamp, or a portable appliance or tool part of a circuit or the premisis wiring system?
A GFCI is not a replacement for a bonded equipment grounding conductor. Outdoors and pool areas especially. Metal cases, non-isolated motors, basically anything with a 3-prong cord cap requires the presence of an ECG, isolated from neutral and bonded back to the panel.