I currently have a light switch that controls a fan/light combo in my bathroom. I would like to change the switch to a double switch that also controls a new light fixture. I would also like to run an outlet that is not controlled by the switch. The existing wiring is 12 gauge on a 20 amp breaker. The wires are round and only contain 1 wire per cable. I ripped all the walls down and only see what looks like a black wire and a white wire with black tape attached to each side of the switch. I found a white wire coming off the fan/light combo that I think I can tie into. Are either of these new connections possible?

Also there are no ground wires anywhere!