With single purchase of any product (theme and module), you are licensed to use the product on one store only. If you are running several stores on a single PrestaShop installation with PrestaShop's multi-store feature, you need to purchase a separate license for each store.
It's okay for you to use the product you bought on a development site. For people who are using our themes, here are two ways to do that.
1. Put the development site in maintenance so you can use all theme features without registering it.
2. Register your theme on the development site so you can use all features. When your site is ready, de-register the development site in the theme editor module or on the Downloads page, and then register your theme there again with the same license code on the production site.