Electrical – wiring switch loop properly

The wires themselves don't have polarity, that only exists within an outlet based on it being wired correctly, or reversed (hot/neutral reversed).

So essentially you just need to identify the hot wires and the neutral wires, and if you maintain this correctly throughout all of the wiring and correctly wire up your outlets, then polarity will be correct.

Non-contact testers are good for determining if there is any power on, but not perfect for finding the hot wire - sometimes neutral wires will give false positives if there is a hot wire in close proximity.

The best tool to use is a multi-meter. The neutral and ground should read 0 (or a very low number), and hot to neutral or hot to ground should give you 120V (assuming your are in North America).

A standard outlet tester will tell you whether the polarity is correct or reversed. If it's reversed, then you just swap the hot/neutral wires.

Short answer, check for continuity between White and Ground.

If you have 120V between White and Black, and White is tied to Ground (check for close to 0 ohms resistance from white to ground), then White is neutral, Black is Hot.

There are some miswired options that may be in play (ie switched neutral), but hopefully this was wired by someone who knows what they are doing.

To answer your other questions: I believe that measuring hot to neutral on a multimeter should give 120V, correct? Correct

What would measuring hot to switched hot give? 120V, assuming that there is a functional light bulb or functioning device plugged into the switched socket. If not, then you would read 0v, or some floating voltage much less than 120V.