Do I need another license key for staging sites and localhost?

No. You can buy only one license key per public site and use it for localhost and your staging site. Your test site url has however to match:

localhost
10.0.0.0/8
172.16.0.0/12
192.168.0.0/16
*.dev
*.local
*.test
dev.*
staging.*
sandbox.*
*.wpserveur.net
*.wpengine.com
*.wptiger.fr

All urls matching the rules above will not be counted against your limit of sites. If you have any problem, please contact our support.