Nothing like that exists in CB nor 3rd party extension that I'm aware of. Moving an entire sites worth of user data from one site to another is not a task for someone without technical knowledge. It requires extensive knowledge of the database structure and where all the relevant user data is located. My reply above only covers core Joomla and CB. I've no idea how 3rd party extensions are structured so I can't really help you there.
It's typically easier to clone your site then work on migrating it to latest Joomla release on the clone. If you want a clean file structure after that you can just point a fresh Joomla install to that migrated database table then begin installing your extensions and your database data should still be there.
Cannot import row 1 because: Incorrect date value: '' for column `joomla_db`.`jdb_comprofiler`.`cb_details_birthday` at row 1
You've a field in your import file with an invalid date format. Fix that value in the CSV or remove the column so it won't try to import. This can sometimes happen if you've an old site that may have really old data structures. Sounds like the field is an empty string so that's probably the case (old data). It should be 0000-00-00 for date fields or 0000-00-00 00:00:00 for datetime fields to signify being empty.
krileon
