How to remove the user registration/how to put a registration on hold 'til administrator confirms it

We have created a website with the Master Study Theme. Since only specific participants should have access to our courses, we want to decide which user can register.

We would like to remove the ability of page visitors to register on the site but retain the ability of users to log in into the page. The idea is to create user profiles manually. Them, the users can use these manually created profiles to log in. To ensure that page visitors cannot registers by themselves, we need to remove that feature from the website.

How can this be configured? We found a way to remove the registration within the top bar, but this also removes the log-in option. Furthermore, on each course page there is an option to rate the course and if someone is not yet logged-in, it links to a registration page. This is a registration workaround that we would definitely have to close, but we don’t know how to do that.

An alternative idea would be to allow the users to register on their own, but automatically put the registration on hold until the admin confirms it. This would require the website to notify the admin via e-mail as soon as a user has registered and afterwards, gives the admin the option to confirm or reject the registration. Additionally, the user should not be able to access any courses while the registration has not been confirmed.

Thank you for your answers and ideas!