There is an option to turn them off, yes. The only limitation is that it's a map option -- you have to turn them on/off for everyone playing in your game -- but I assume that's not usually a problem.
The same way, as far as I know -- while you're connected to the server, if you're an admin, you should be able to change the setting.
If you're supposed to be an admin but aren't (i.e., you've never set yourself up as admin on your server) and you have access to the server console, type /promote MainTango into the server console. Otherwise, you may need to look up how to set up admins on Factorio multiplayer; beyond the above, I haven't needed to.