As someone who travels to SCL many times per year I can tell you that you can definitely leave between connections but be careful because security can be a drag at peak times. I am not sure how much the reciprocity fee is for Europeans (if there is one) but I know its $100 for Americans (once per passport) and $250 for Canadians.

I always tell people to check out Las Condes if you are looking for a nice afternoon stroll but it depends how much time you have. Feel free to message me if you need some restaurant recs or any other specific questions.