Having a VPN for players to connect to your server and eventually seeing the website, I guess that's not a public server anymore and it's a huge headache, but yes, in other words you'll be having a private server under a private network.
Once your server is public, you can't hide the identity of your server. Hiding payments worked a few years ago, but not anymore. PayPal and any other payment gateway are asking additional information which they will verify sooner or later.
More or less, usually private servers (in any other MMO) DMCA takedowns and notifications are usually on the servers where the host is earning money through donations. There's unlikely to be taken down if there are no donations and your server is free to play and play to win, but not always true, of course.
The ones who can take you down are the 3rd party publishing company and licensed by the development company and ofc the development company.