2. To actually use the contactless, do we just open the Apple Wallet to the registered card as we would do with any standard Apple Pay merchant and go? Or do we still need to use a physical card or Apple Cash? Just want to know what we actually do as we walk up to the turnstile.
Yep, that's exactly what you do. No physical card necessary (unless your physical credit card has the contactless symbol on the back, of course, which might arguably be less hassle than trying to use your phone).