I've been using mine a lot for the past couple months at Peet's, 7-Eleven, Petco and somewhere else.
In my experience, "tap" means physically touching the other reader. Not rubbing it around like a massage, just lay it on the reader's scan pad until the phone vibrates, beeps, and flashes the "Sent" message. This is not only my experience with PayPass, but with NFC phone-to-phone handshakes with my wife's GNex, too. When they refer to the technology as "Near Field," they're not kidding! (Mine is communicating though a thick Otterbox case, for whatever that's worth.)
At point of sale, you'll never be prompted to select which card to use. Under the Payment Cards icon of the app, whatever card you've currently selected as the Default will be the card that's used.
If the phone is unlocked and you use it on a PayPass terminal, but don't open Google Wallet first, then the Wallet app will automatically open. If you haven't unlocked Wallet with the PIN code inside of the timeout period you've selected in the GWallet settings menu (1, 5, 15 or 30 minutes), you'll be prompted to do so.
On the other hand, if you have opened Wallet and entered the PIN, you can back out of the app (as long as you don't hit the Lock icon in the upper right corner of the the screen), perform other tasks / open other apps, and even lock the phone, and Wallet will remain unlocked and ready to pay -- as long as the phone is unlocked, and as long as you haven't exceeded Wallet's PIN timeout period. This prevents you from having to enter your Wallet PIN when you're most likely to have an audience of the curious looking over your shoulder.
Because this NFC "looks like" an NFC-enabled credit card to PayPass readers, whatever signature policy the store has is going to most likely apply to Google Wallet usage. So far, the only place I've had to sign my name was on a paper receipt at Petco, for a $60 purchase. It was unexpected only because I wasn't asked for a signature any other place I've used it, but those places don't require my sig for traditional credit card purchases, either.