You have asked a couple of great questions. And Charles Darwin himself was one of the first people to try to answer them!
Coral reefs form in the warm shallow water of the tropics, all over the world. The animals that make coral reefs, the corals themselves, can only survive in water that
is warmer than about 70 degrees all year. Since the ocean gets much colder than that here, corals can't live in California. But, the water in many other places (like Hawaii) is warm enough and it is in these places where coral reefs
Coral reefs are made up of millions and millions of individual corals, who live in
colonies. Each individual makes a small external skeleton of calcium carbonate, the same thing that clam shells are made from.
Each individual skeleton is attached to all the others, and so while each animal doesn't make much, the entire structure can be huge. Imagine looking at a single brick (like an individual coral) and comparing it to a huge brick building (the coral reef).
There are lots of different kinds of
corals that make up a coral reef, and each kind
grows at different speeds. Some grow very slowly (less than 2 mm per year, or 1/10th of an inch), but others can grow much faster, up to 10 cm per year (or 4 inches). Since the reefs are made up of all of these different kinds, the entire reef will grow pretty slowly, usually around 1 cm per year (a little less than 1/2 inch). It seems to me like coral reefs form at a pretty slow rate, but it really depends what you are comparing it to!
The corals grow throughout the year,
but they seem to grow best when the water is warm
and clear. They probably grow best during the
summer, whenever it is summer where they are
growing. So coral reefs are continuous growing, forming and changing. But since they grow so slowly, it is really hard for us to watch this process. Still, scientists estimate that some coral reefs may have been growing continuously for over a million years!