PHP 7 is still very early in its development cycle. A lot of extensions I wager will not 100% work with it. We've still a few bugs with PHP 7 due to depending on Guzzle API library for HTTP requests. We've already made plans to move our minimum PHP version to 5.6 most likely, upgrade all our dependency libraries, and we'll be able to 100% stable support PHP 7. In short for a basic usage yes PHP 7 with CB is tested working fine, but the more advanced of an install you configure the more likely you are to hit some sort of PHP 7 issue.

Personally I recommend sticking with PHP 5.6. Then clone your install to a PHP 7.1 test environment after everything you want is configured and test to make sure it continues to work fine. If it does it's safe to assume upgrading your live site to PHP 7.1 will be fine. If not then please report any CB related errors you find.

CB is not 100% PHP 7 compatible yet. We've 3rd party libraries that are not PHP 7 compatible that we can't update until next CB build release where we'll be pushing minimum PHP version 5.6, updating those libraries, and should be able to move development environments, etc.. to PHP 7. I recommend continuing to use PHP 5.6 for now if possible.

My current site is Joomla 3.6.5 which is installed on the localhost prior doing the new site and has the latest CB and CBSubs but they both crash when selected in the admin panel with the following error message: Fatal error: Redefinition of parameter $user in F:\NewSite\htdocs\components\com_comprofiler\plugin\user\plug_cbreconfirmemail\cbreconfirmemail.php on line 134

There is no such usage on line 134. Update CB Reconfirm Email and retry.