adding light switch to an existing circuit
I don't see a problem with that.  

Right now, the cable between the switch and receptacle has 2 wires besides ground: 


Always-hot   (white, and it's supposed to be marked with tape, and it's not)
Switched-hot (hot when the switch is on; on yours, native black). 


Your new wire assignment on that segment will be (and the colors are mandatory): 


Neutral -- actual white
Always-Hot -- black


That's exactly what you need there to continue the circuit in the conventional way. 

You will need to rearrange the wiring in the old receptacle box.  Remove all the non-ground wires from the old receptacle. Put a 6" black pigtail on a brass screw and a 6" white pigtail on a white screw. Then wirenut all the white wires together... and all the black wires together... regardless of how they were arranged before.  That should make the receptacle work at all times.