Do your ponies have to be married to breed on PonyStars

No. They don't. You can breed your ponystars with each other by going to the male you want to breed and clicking Stallion Status. Then look where it says proposals. Pick the female you want him to breed with and click Request. When you've done that, go to Proposals on the left side menu. Then click on Received Requests and click Accept. Hope this helps! Oh, sorry, but I DON'T know how to breed with other people's ponystars. I'll try to find out!