FOSS gamedev and creative worlds

Is it possible to host a Server on a web host?

HTTP web hoster -> no
VPS -> yes

Okay, thanks. Is there a tutorial to hosting on a VPS server?

Maybe for testing or a small private server with only 2-5 simply users it works with a hoster like https://www.webfaction.com/. But you have to compile everything yourself and take the necessary precaution measures in order not to use too many resources (otherwise you may get kicked).

My own experience (what works) are:
* 3-5 players (everyone 4-6h activity in a week)
* RSS memory (while players digging and walking around) stays between 300 - 450MB
* Database size around 280MB (it seems memory grows with database size, or my players just tend to running around)
* Single CPU usage stays around 20 - 99% (depends what they do)
* A few mods (even mobf works, but without monsters and other cpu intensive tasks [pathfinder])

Web hosting is not suitable for hosting a minetest server.
If you want to host a (small) Minetest server, a VPS with 512MB RAM should suffice.