Will version 2.82 install in XP SP2?
If not which is the latest version that will?


The easiest way would be: install it and see if it works.
Also see:
(which says ... XP SP3)

btw., you know about product life cycle?
Microsoft End up support XP SP3 since a long time, Vista since April 2017.
Hope these machines are disconnected from local network and internet.

If these machine is still needed, you should think about an update.

as usal, every operating system is just supported if latest paches are installed.