Hello,
1/ I can’t open your Shop page.
Try to disable all the third-party plugins (including cache plugins), that do not come bundled with XStore https://xstore.helpscoutdocs.com/article/36-included-plugins , clear cache of browser, and check then. Maybe one of the additional plugins is a reason for the problem.
If this situation is not caused by a plugin, contact your hosting providers and ask to give you a server error log to check what is wrong.
2/ To enable registration, navigate to Settings > General > Membership and mark Anyone can register, then go to Woocommerce > Settings > Accounts > Customer registration > Enable customer registration on the “My account” page.
Read more about settings – https://docs.woocommerce.com/document/configuring-woocommerce-settings/#accounts-and-privacy-settings
FaceBook and Google login – https://xstore.helpscoutdocs.com/article/87-facebook-login
Regards