Question

Aside from earth, how many other planets in the solar system have layers?

Answer 1

Mercury, for instance, does not even have an atmosphere, so could not have any ozone at all.

Mars hardly has any oxygen, so could not have enough of what it takes to make ozone. Venus atmosphere is nearly pure carbon dioxide; so again, it lacks the stuff to make ozone. As for the gas giants (Jupiter, Saturn, Uranus and Neptune) their atmosphere is mostly hydrogen and helium, with traces (less than 1%) of methane, ammonia, water and other compounds. With that much hydrogen, ozone would immediately react with it to form water.

So, it seems that, in the solar system, only Earth has an ozone layer.

I hope you are talking about the ozone layer