You do not need to install a license for JBoss EAP.
Registering a JBoss instance is not necessary.
Yes, You have to purchase a valid subscription for JBOSS EAP 7 enterprise Application server in production environment
If you want to use the community version of Jboss EAP 7 , then you can download wildfly 10 (free of cost , no support provided for wildfly) from Downloads · WildFly .
Wildfly 10 is the latest community version of EAP 7 which has high performance and new security features.
If you want support for your JBoss EAP 7 , then you have to buy JBoss subscription , no any software license is required for that , you should only have a valid subscription.