How Can I Know The Age And Sex Of My Goldfish?

You can tell a fish's age by counting the rings in the otoliths, a type of bone in the fish's head, however to do this you'll need a microscope and a dead fish. As far as I'm aware, there is no way to tell the age of a fish for sure while it's still alive. There are measures of length which are attributed to ages but they can be off and some fish will just be bigger than others. Usually goldfish are over 8cm long before they can breed.
 
Males will get something called "nuptial tubercles" which kind of look like white pimples when they are in breeding condition. Only the males get these so it's a good way to determine sex as well.
 
Good luck!

The breeding season is in spring or summer. Good luck breeding your fish!

I don't know about age but to tell the sex you have to look at their bottom fin,
a girl's bottom fin is triangle shaped and a boy is kind of a line