Assuming the wires are the correct gauge for application and breaker you use black and white wires as hot. Put red electrical tape on each end of white wire and connect red and black to the breaker output and bare wire to ground lug in panel. At receptacle connect black and red to hot contacts and bare wire to ground lug.
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Receptacles are not wired in series. Receptacles are actually wired in parallel, what this means is that all phase wires (black) in a receptacle's box should terminate to the brass screws on each device, and all neutral (white) wires in the box should terminate on the silver screws on each device.
If both wires are black then the one with the writing is the neutral wire. If the two wires are black and white then the white one is the neutral.
Black/White/Ground power in and the same out. Tie the incoming and outgoing white wires together under a yellow wire nut and push them back in the box. Tie the ground wires together under a green wire nut and connect the pigtail from those ground wires to the ground screw on the switch. Connect the 2 black wires you have left to the 2 screws on the switch. Doesn't matter which black wire you connect to which screw.
It is because the nec standard.
You will have to run new electrical wire or a single ground wire back to the panel (though the former is highly recommended). A GFCI outlet will cut off the circuit if it senses voltage leaking to ground. If there is no ground wire, it will not function.