Yes, except in the Swedish phones, where the numbering starts from 0. So dialing 0 would make 1 pulse, dialing 1 would make 2 pulses, and dialing 9 would make 10 pulses.
That's more like "ever since digital mobile phones came around". The number 112 is in GSM standard.
Technically, the network gives it a priority, and you can make a 112 call even without a SIM card, or even if your operator does not have coverage. The call goes through any operator that has coverage. (You can actually see this in the phone display when making a 112 call; it handles it quite differently. I have done it a few times; unfortunately, most of those times, someone has died...)
If the network is so busy that all traffic channels in GSM are occupied, and you make a 112 call, one of the existing calls is dropped and you get the emergency call.
This had some interesting side effects in China. There, prior to introduction of GSM, the number 112 was allocated to phone company technical complaints. Police was 110 and fire alarm was 119 and so on.
So, if you were making a GSM phone call to a friend, and the network was full - not that infrequent in China - you wouldn't get through. But you could call the technical complaint line at 112, and this was a priority service which dropped one of the existing calls. Once the technical complaint service was ringing, you could drop that call (to the network, an emergency call) and you'd have one free GSM time slot in your cell. And you could call your friend.
Until the next guy did the same, and your ongoing call would get mysteriously dropped.
The plot point in question was that they were encoding the phone number when leaving it as a callback number. Pulse dialing wouldn't have come into it.
Edit: Just realized why a zero is in the '10' position on a rotary phone. Huh.