Change what percentage/time remaining causes the battery icon on Mac to go red
...how I can, if possible, change the percentage of battery remaining
  that will cause the battery icon to turn red in the Menu Bar.


You can't.

It's not something that can be modified.  

The battery icon changes to red when you have less than 15% charge remaining (macOS 10.8 and earlier).  It changes when there is less than 10 minutes remaining in Mavericks (10.9 and later).  See About Mac notebook batteries

You'd need a 3rd party app like Coconut Battery (Paid edition) so you can get notifications when your battery reaches a certain level.  

(IMO) If you're going to pay for an app to tell you this, just buy a new battery and be done with it.