Hello Caro, "off" as an adverb could mean something is not operating, removed or not at work, but in your sentence it is rather the phrasal verb " go off " . "go off" as a phrasal verb could mean ( as in your context),when a warning device goes off, it starts to ring loudly or make a loud noise " a smoke alarm went off " A smoke alarm started ringing loudly and making a loud noise. That is why DP froze and didn't know where to go ;)

That can be very confusing for someone learning English. Usually the term "to go off" means to -turn on- or -to start-. In this case, the smoke alarm went off, meaning that it's alarm started. Another example would be, my alarm clock went off at 4 this morning.

"went off" means that is started or triggered. It is an idiom. If an alarm goes off, that means it starts sending out whatever signal it's supposed to - by loud noise, light or message. If a bomb goes off, that means that it explodes. You are right that "go off" would most logically be interpreted as turning off. However, as we all know, language many times is totally illogical. If the alarm turned itself off or turned itself off, we would say that or "the alarm stopped".