Yes, the stove was functioning. It is from the 50s, before liability and person injury lawyers ruled the world and you could actually buy toys that might *gasp* harm a tender young finger. Maybe kids just had more sense in those days, I imagine if you burned your finger once you wouldn't do it a second time. The sink also had a little pump so water would run through it.
The rubber glove was a promotional sample given away by rubbermaid. I wish I had two of them!