First of all: Learn to Script

Above all I suggest you 2-3 tutorials in Shell-Scripting, so you get familiar with the necessary environment in order to be able to write the scripts, which are executing the necessary actions.

Here are some hints for an easy start:

Don't reinvent the wheel - use a monitoring system

My first thought is, that on every linux server that is managed this way a monitoring should be installed. This monitoring is configured for the relevant paramaters that your task needs. And if one the parameters is bad an action(e. g. a little script) should be executed, which fixes the situation.

Of course you do not need a monitoring system at all. You can script all the way through with your own scripts. But if you use a monitoring system it will be far more stable and feature rich than your own code, especially as you are now at the beginning to learn scripting.

The windows machine is of no use here - imho - because monitoring is nothing which must be started on demand. Monitoring is running always.

All major monitoring systems - by design big software packages to monitor many servers - can initiate custom actions on flexible defined failed checks. But those systems are very feature rich and so you need your time to get familiar with it and to learn how to use them. Pure Nagios is feared for its hell of config files.

Monit - a simple monitoring utility

A monitoring system which is far simpler than the other heavywheights is Monit and specially designed for simple monitoring and actions. I could imagine, that this would be the tool, that helps you most with your current task.

Check_MK

Personally I'm using check_mk - a full featured monitoring suite based on Nagios. I like it very much. And I recommend it if you have at least about 20-30 servers or more to monitor in detail - but of course "Server Monitoring" in whole is not your task. And of course I'm triggering a bunch of maintenance actions to fix various server problems.

Use an existing monitoring system?

Maybe your environment has already a monitoring suite( I suppose not ), which you can use to trigger the needed actions? Ask your colleagues!

Update-1

Maybe some simple cronjobs run once a day or once a week can help you too.