Can I use Red Hat AMQ 7.7 in production without license or support subscription? And what's the difference between JBoss AMQ and Red Hat AMQ?
All the projects which are part of Red Hat AMQ have open source licenses so there is no problem with building and using them in production. I don't believe there is anything legally stopping you from using any such version without support. Without a valid subscription you won't be able to use the specific bits distributed by Red Hat. Without support and easy access to the bits I don't really see why you would use Red Hat AMQ as those are arguably the two largest benefits. You could easily just use ActiveMQ Artemis directly instead.
At the end of the day, I am not a lawyer, and I do not represent Red Hat. I strongly recommend that you discuss the issue with Red Hat directly.
Red Hat AMQ and JBoss AMQ are the same thing. The "JBoss" branding was used prior to the most recent AMQ releases.