Does it works with Nginx?
Yes, Hide My WP supports Nginx. You need to have write access to Nginx config file. Please note, using Multi-site on Nginx is not officially supported yet but if you can convert htaccess rules to Nginx you may make it work.
We do not officially support a mix of different web servers. (e.g. Apache alongside Nginx) but based on your knowledge and setup you may make it work. (Just several rewrite rules)
Update: Multisite Nginx and IIS are in the plan.