Are you thinking of plain glasstop stoves? Those are just coil stoves with a layer of glass on top.

Induction stoves are the ones where the surface stays cold.

Glasstops are as you describe.

Sometimes, but only on very quiet roads.

I find spoken word works a lot better, because I can find a volume where I can still hear the road. With music, I can hear either the music or the road but not both.