To answer your first question "How do you tell if the faucet has this
device or not?" the test is quite simple.

Turn the shower on to a lukewarm to warm temperature and hold your
hand in the flow as someone flushes the toilet. If the shower output
gets suddenly hotter as the cold water fills the toilet, it is not an
anti-scald device. An anti-scald fixture senses the change in pressure
on the cold (and/or) hot side and rebalances the output to keep the
shower temp constant.

of course this test assumes anti scald is working..........

if its broke you still wouldnt know for sure