If I purchase a Sitefinity license (used on a production server) will I need to buy additional licenses for development and testing servers?

No, you don't need to purchase additional licenses because every Sitefinity license comes with unlimited number of sub-domains for non-production purpose such as development, testing, staging, etc. Please, contact us and we will issue you the respective license keys. Note that you can use the localhost domain for development purposes with any license key.