Hello,
1/ 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
2/ I’ve checked via incognito browser – https://prnt.sc/22kpwm7
Regards