Inside of the cookies turn up soft, almost uncooked?
Don't use the pizza stone for cookies.

Stones absorb a ton of your oven's heat and will really mess up your baking times. They're designed to be preheated in your oven before you ever put a pizza (or other item) on them. I have never tried it before but you might be able to use the pizza stone if you preheated it but then you have to put your cookies on a hot surface which may cause them to misbehave in other ways.

Cookies should be baked on light-toned heavy-duty metal baking sheets (or as close as you can get to that) because the metal transfers the heat, it doesn't absorb it.

That's how you get well-baked cookies.