No, it is not a proper noun.
No
The word evolution does not need to be capitalized.
No, coral does not need to be capitalized.
No, circa does not need to be capitalized.
No, it doesn't need to be capitalized.
No, kinetic energy doesn't need to be capitalized.
Yes, "Ozone" should be capitalized as it is a proper noun referring to a specific molecule composed of three oxygen atoms.
The word evolution does not need to be capitalized.
No, coral does not need to be capitalized.
No, it shouldn't be capitalized.
No, circa does not need to be capitalized.
No, it doesn't need to be capitalized.
We have to cure ozone. To cure ozone we need to stop using ozone depleting substances.
No, kinetic energy doesn't need to be capitalized.
It should be capitalized if it follows or precedes a name.
Yes, the 'A' in AIDS should be capitalized as it stands for Acquired Immunodeficiency Syndrome.
Ozone layer is depleting. We need to protect it.
You cannot be stuck in ozone. So there is no need to get out.