Nah, probably not. All routers you can buy today will route and by default have their firewall active. Make sure, auto-updates are activated on your router.
Check your server OS'ses and the Software running on them for updates on a regular basis - since they are partially made available to the public and are potential attack vectors.
Though if you only port-forwarded a couple ports that dont include the RDP port or something wildly stupid, you should be safe.
Follow some best practises as:
- try to dont run your Gameserver Software as administrator but instead with a account with as low privileges as possible.
- update your OS'ses, Softwares and Router/FW Appliance.
Don't let yourself fool by the guys telling ya to setup a full fledged firewall system when you obviously don't even know basic networking. You would be overwhelmed by the configurationpossibilities.
If you want to dangle your foot in some cold water - try em out and put some machines behind them to learn what behaves how. But dont make em your only protection against the public internet when you don't know basic networking stuff.
Happy Sailin' matey!
I would guess, a monitoring system like CheckMK or Icinga?
You could check what has been alarming even if the check is green again, by the time you look into it.