I am a little confused? You bought her a MBP and that is not the machine you are having a problem with? What year is the MBP and what size?
I am gathering your problem is with a 2017 air?
If the fan is constantly running and it is slow it could be that the cooling system is blocked with dust and debris. It could be that the applied thermal paste has gone bad or both.
If you have wiped and reinstalled I am going to assume that it is not a software problem.
If you can open the back of the Mac to see if the vents are blocked and check the fans. Vacuum them out, get some dry paper towels and wipe things down. Get a can of compressed air and clean it out.
If it looks clean and there is no blockage or debris then it is probably imminent hardware failure. I am not sure if this model has an ssd or hdd? If it has a spinning hard drive it is most likely failing and could be the problem. If it is an ssd then run hardware diagnostics.
Also you can call apple and even out of warranty they should be able to run a remote hardware diagnostic on your device. Have them run the diagnostics and let you know the results.
There could be a few reasons for what is happening. Cpu failure could happen but more than likely it is just a blocked cooling system. Intel cpu run hot and need constant cooling. If they don’t have decent cooling everything will slow down as the cpu throttles down to prevent catastrophic failure.
If it has a hard drive and not a ssd they often fail as well and they will also slow everything down and the cpu has to work harder just to do basic tasks. A replacement for hdd or cleaning the cooling system is most likely.
Lastly your cpu could be dying but I think that would be unlikely. I am sure there is still life left. I am not sure if the 2017 has modular ram or not but if you open up the laptop and you can replace ram you might want to add more ram and possibly replace the ssd. I am not sure what is soldered to the board but if you can replace it might be a good idea to do so. First make sure it is not the cpu causing issues and get apple to run hardware diagnostics remotely by phone.
Good luck!