Locking down and forcing login to Sub-site

Hi all!

I have got a Multi-site running and would like to lock down the Sub-site and only allow pre-defined subscribers & admins to be able to log in.
It would be great if I could also lock the possibility of showing https://sitename.se/sub-site in the web browser. I alway only want to show https://sitename.se/ whatever page or subsite page I am on.

Also I want to block the possibility of browsing to the sub-site by typing https://sitename.se/sub-site/ if that is possible.

Anyone got good ideas? I am rather fresh to WordPress so I am no experienced user.