How to use on an existing web server?
I would love to use your panel, it looks very great, is free and compatible with BungeeCord and PocketMine.
I have an existing server where I'm running Plesk (All-In-One server control panel with web server (apache)).
Can I install PufferPanel without damaging Plesk and existing domains? How?
And another question: is it possible to install the web interface in its own directory, so for example that I can put the web interface files in my domain folder that I can reach the panel from panel.mydomain.com?
PufferPanel does not generally work well with panels like cPanel or Plesk. Our installer uses nginx, which I know Plesk may use as a front end proxy, but you would have to configure it to handle PufferPanel manually and I do not know if Plesk would like that very much. I would recommend using a different server especially if you are not comfortable fixing any issues it might cause.
You certainly can use a subdomain with PufferPanel, most people do. Make sure you create an A record pointing to the IP where you are going to install PufferPanel, and provide that domain to the PufferPanel installer.