Battlegrounds Games

On BGE is there no fog of war option?
Does the system adjust the players stats if hit in an attack or healed? or does this have to be done manually?

No, BGE has no Fog of War feature. BRPG on the other hand, does, and you can see an example of it in use in the first two screenshots listed here.

Neither program automatically adjusts stats. That is generally tracked by manually editing the values in the Turn Sequencer.