Hi ! Online multiplayer template uses PeerJS server, which is a public server open for everyone, it helps to establish connections between PeerJS clients. So if you get the template, you will also get the server with it, it's a public server.
The delay depends on how far are you from the server. You want to change the game from top down to platformer ? In that case, you need to adjust the events, and other related mechanics, since the template is designed for top down