How can I wire a new outlet from a light switch, with light switch set-up I've never seen before?
I was taught to feed the hot from the top. It could be the bottom or top. Get a noncontact voltage tester to see which one is hot with the switch in the off position. Trial and error will work here as you only have 2 choices and it will not hurt anything to use the wrong one your outlet just won’t work when the light switch is off. Other than that yes White to White, Grounds all tied together.
Make sure your new wire is sized right, 20A breaker 12 gauge wire, 15 A breaker 14 gauge wire. (you can use 12 gauge wire on a 15 amp breaker just not the other way around).