If you want the stats to stop resetting after each battle, set a variable that would prevent it from calling the script after the first time it's been called, then on player death reset that variable.
Something like:
If newgame=false
call stats script
set newgame=true
else
The same goes for the enemy. On the battle scene, if enemy HP hits zero, have it trigger a new variable. Then on the map scene, before the screen fade-in, have it deactivate the actor if that variable is true.
To set up a battle system is a bit on the intermediate side. I would recommend getting familiar with the basics of GB Studio. There's a lot of videos on YouTube, I have made a few as well.
I am currently working on creating a full starter kit to help people get up and running quickly, but it will be a while longer before it's ready.
If you have any other questions please don't hesitate to ask.