My dad told me that steam can only exist under pressure and is invisible. When released it becomes (very hot) water vapor. Is this water vapor cooler than 212 degrees?

Well, it depends on the situation.

Under atmospheric pressure (the 'normal' pressure of the air), steam will only form when water boils at 100 degrees Celsius (or 212 degrees Fahrenheit).

However, if you boil water under higher pressure than atmospheric pressure, the water will boil at even higher temperatures.

You can see it like this:
The water particles need energy to escape from the liquid water. Since there is greater air pressure forcing them back into the liquid, they need more energy (more heat) to escape. Once they escape, they can be at temperatures higher than 100 C (or 212 F). This is still called steam.

Similarly if you can have an air pressure below atmospheric pressure, the water particles will need less energy to escape from the liquid. The water vapour will then be cooler than 100 C (or 212 F).

One more thing, is that we commonly refer to steam as the white 'fumes' that you see when water boils. In fact, steam itself is invisible. It is only when it cools down, and become tiny drops of water that you see it as white 'fumes'.

In general, water vapour itself does not have a specific temperature, like water. It can exist at various temperatures if certain conditions are met. But that, you may not understand quite well at this level, but it's really interesting to know about these.

Sorry for the long post :o, but if you have any more questions, you can ask here :)