Please ensure you've reviewed Joomla documentation/tutorials carefully for your migration as there is changes between 2.x and 3.x. Please see the below.

docs.joomla.org/Joomla_2.5_to_3.x_Step_by_Step_Migration

As for CB there's no differences between the API we're using on either of them. CBs registration page only shows that error if registration has been disabled. Within CB > Configuration > Registration ensure CBs registration is set to be independent from Joomlas then disable Joomlas within Users > User Manager > Options.

Your userlist not showing users is likely due to your userlist not having any columns configured. Edit your userlist within CB > List Management and ensure there are columns configured under the Column tab. If it is configured then check if you're using CB Privacy as it will remove user rows based off the Profile Privacy of the user.

Please PM backend super administrator login credentials and will take a look.

You set the Default template and CB Core to Registered Access. This means Public users can't access core CB features. I've set them back to Public and everything looks fine now. Please also confirm is working fine.

Note in your screenshots you got an access denied error on registration due to accessing registration while logged in. You need to logout to access registration.

It also looks like you've a bunch of plugins that exist in the database, but don't exist in the filesystem. Those are all the grayed out plugins in CB > Plugin Management. You should either install the latest release of those plugins or delete them.