A user with a free plan is still a user. Meaning they still have a profile they can access, etc.. You control what they can access using your new usergroup and its view access level as needed. So for example if you've a tab you don't want them to see then be sure to set the tab to your new view access level. This should apply all throughout Joomla as well.

Regarding a custom login redirect based off their subscription you can control that directly in your CBSubs plans. First edit all your CB login modules and empty the login redirect. Next in CB > Configuration > Registration empty the first time login redirect unless you want to send everyone to the same page for first login. Now edit your CBSubs plan and under the Workflows tab adjust the "CB Login workflows" parameters as needed.

The registration form for the registered user for plan #2 is not processing correctly I still get the original error message that started this post out. A subscription is not created for the user attempting to register.

I'm guessing you've an ACL configuration issue somewhere in the attempt to basically lock out a free user as a guest user (which can't work as per Joomla permissions). Both of your plans should have "Visible for Access Level" and "Visible for Group (and above this group)" under the Access tab set to Public to ensure access. The Subscription tab within CB > Tab Management should also be set to Public. Finally CB Paid Subscriptions it self in CB > Plugin Management should also be set to Public. If still not working please PM backend super administrator login credentials and will take a look.