Is Thunderbolt on the same bus as FireWire and Ethernet on a late 2012 Mac Mini
After a lightning strike the Mac Mini FireWire and Ethernet ports do
  not work.


The Mac mini got hit by lightening and still functions?  I am surprised that you only lost two ports


  Is it likely that the Thunderbolt port is also burnt out.


Likely, but it's  impossible to tell from this distance.  To know for certain, you need to plug in a device to test functionality.


  I am proposing to use a TB/FW adaptor.


This sounds like an excellent idea.  If you plug it in and it works/doesn't work then you have your diagnosis.    

The only other suggestion other than trying things to see if it works is to run Apple Hardware Test (AHT).  Hold the D key while booting from a powered off state with the AC adapter connected.  

However, it sounds like you lost some key functionality when the Ethernet port died.  It's probably a good time to take it in for service or upgrade to a newer model.

On a side note, a good (and cheap) bit of insurance is to get a UPS Back-Up Power Supply with surge protection.  I personally use CyberPower UPSs on all my Apple gear (APC everywhere else) because they are compatible with macOS.  

Speaking from personal experience...in 25+ years in IT in the lightning capital of the US (Florida), I have been hit by lightning twice and never lost a single piece of gear.  I did lose two APC units to lightning strikes (both at work), but I never lost any equipment.