SSH/SFTP can be used to install game server modifications. We do not recommend changing or moving anything without understanding what those actions may break. Game server backups of your game servers will include the modifications that you installed for that particular game server.
Our Rust servers support Oxide/uMod modifications and can be easily modded through it.
Check out Oxide/uMod's website to see if your game is supported.
If you brick your game server, you can always change your hosted game to factory reset your server.
MineCraft modifications can easily be installed. Visit the MineCraft wiki page for more information on how you can install mods onto your MineCraft game server.