I'm from Tunisia. I will go to Amsterdam. Can I leave the "international zone" and go out of the airport and then come in again? Does anyone care and will they let me in again?
Are you concerned about visa issues, security checks or potential fees?
To go out of the international transit area, you need to go through a border checkpoint where the police (I think it's the Koninklijke Marechaussee) will check/decide if you have the right to enter the Schengen area (for a Tunisian national, it most likely means having a Schengen visa). In Amsterdam, I have also seen police officers directly at the gate for some international flights, checking visas and ID right out of the jetway, before entering the terminal itself. You also often have to wait longer if you don't have an EU passport.
If you go further out, through the baggage reclaim area, you will also go through a customs (douane) checkpoint. Most of the time, you don't have to do anything but you might have to answer questions, open your bags, etc. to show you're not importing anything illegally. Once you have done that, you can easily leave the airport, explore the country or even go to neighboring Schengen countries.
Then, when catching your onward flight, you will need to go through a passport check (again, possibly longer for non-EU passports) and a security checkpoint (x-ray/metal detectors) to get back to the “safe” area of the airport. You will also obviously need a boarding pass and enough time for the whole procedure.
Since your carrier will typically already have checked your right to go to your final destination and provided you with a boarding pass, getting back in should not be a problem but getting out might be. In any case, it doesn't really matter if it's for a few minutes or a few days, a great many people are paid to care. On the other hand, if you do have the right visa/passport, getting out is no problem and you will not have to pay anything just for that.