Questions about managing groups in groupJives.

Hello,
I have a group of users A (free) and a groups of user B (paid by CBsubs)
How to:
Have a members of Group A be able to see the titles of forums, but not enter or write.
Have a members of Group B be able to create forums, write inside, and manage members.
Have a members of A be able to request to enter a Group B forum.
They will then be able to see the messages but won't be able to write until they join Group B (paid).
Thank you.

GJ group forums are not accessible or visible unless you're a member of that group. There's no working around this due to the permissions system in place in Kunena.

As for member management and users requesting to join groups that should already be doable out of the box with GJ. Set your groups to Approval type to require users to request to join. You can protect the join process using CBSubs so a subscription is required to request to join as well. This is done by using By URL Part protection and protecting the following.

option=com_comprofiler&view=pluginclass&plugin=cbgroupjive&action=groups&func=join

Ok, but practically, the group permissions in GJ are done with the modules: CB GroupJive and CB Subscriptions?

Group permissions are controlled by the group. If you're not a member of the group you cannot create content in that group. If the group is publicly visible then they can see the groups content but not interact with it. The exception is the forums integration since Kunena doesn't have a permission to view topics, but not access topics so it just blanket protects the groups entire forum category. There is no getting around this unless you modify CB GroupJive Forums I guess and remove this protection and implement your own.

You can of course protect the ability to join groups with CBSubs using the By URL Part usage explained in my reply above, but they're not going to be able to see that groups forums until they join. I'm not really sure why you want them to see topics they can't even read though to be honest.