First, make sure you've disabled the JomSocial Facebook integration by removing the API/secret keys from their Facebook Connect section. Then, yes, change the registration mode to "Normal" and make sure the JomSocial - JFBConnect profile plugin is enabled and configured. Sounds like you are at this point already, but good to say it.
As for the API error issue, can you try the following, in order, and test after each. We'll need to narrow down what setting is causing that error:
1) In the Profiles area, disable the avatar import.
2) Undo all field mappings.
3) Hide all fields from registration.
4) Disable the JomSocial plugin altogether
Hopefully, after one of those steps, the issue will go away. If so, let me know what setting 'fixed' the problem and we can narrow in on why that issue is happening and how to re-enable it without problems. That should also, hopefully, help you start testing the full flow with that one setting disabled.
Hope that helps, and keep us posted, as always,
Alex