You only needed three tests.
A to B
A to C
B to C
You are testing things like A to A. Does that mean you are touching both probes on the same terminal? If you touch the same terminal with both probes, it's the same as touching the probes together. That will always give a reading on the meter. Also: A to B is the same as B to A. You are running wild brother.
In a continuity test, the meter is passing a small current thru one of it's wires and wants to see if the current returns to the meter thru the other wire. If it does, it displays a number on the screen. It does not matter what the number is, Just that there is a number. THE NUMBER CAN BE ZEROS. If you touch the two probes together, obviously the current passes back into the meter and you see a number. That's why you touch them to see if everything it working before testing something.
If a person has two ends of a wire but doesn't know if the wire is broken somewhere in the middle, they do a continuity test. They touch the black probe on one end of the wire and the red probe on the other end of the wire to see if they get a reading on the display screen. If they do, the wire is not broken. In your case, you are testing to see which terminals are "connected" inside the switch when the switch is off and when it's on.
Most meters show a "1" when you set them to test continuity. In other words when you turn the meter on. This means "no continuity". If the "1" changes to zero (000/00/0) or near zero, when you touch probes to something you are testing, or touch probes together, it means there is continuity. Current is passing thru and back to meter. I know it's weird that zeros mean continuity.
Please advise if the meter displays a "1" when turned on/set for continuity.... or displays "OL".
We are trying to find out which terminals are connected inside the switch (showing continuity/a reading on the meter) and which are not.
Also, I don't know what a reading of "nothing" means. Zero's or screen is blank? Looks like using 200 ohms is the best setting. So now explain what "nothing" means. I expect that when you turn the meter on, you see some sort of number.
Next: same test with switch ON.
A two position switch means there is OFF and there is ON. It does not mean there is Off and then two positions. If "nothing" means you got 000, you had the switch "ON".
Continuity can be used to find a short to ground. A whole other story.
