Security and Admin

I have some security concerns for my wordpress site and would be so very grateful for advice! I am using Wordfence, and saw today in Live traffic, that I am constantly being “attacked” by IPs mainly from Russia, but other countries as well. Especially Russia, it says about scanning my site about author page etc. I chose to discourage my site from being found by search engines, at it is a fully private site and password protected, only given to selective people. I am very concerned about all the robots, robot txt etc, and need my entire site and all my pages from being indexed/ I am not familiar with the procudure and will be ever so thankful for help! I need my site to be accessible for those to whom I send my password and otherwise neither to be indexed nor found. Could someone please help me?
Thank you!