You can in fact bake a cheesecake with parchment paper. The only thing that may be an issue is that the cheesecake may stick to the paper. In this case, you can lightly grease the parchment paper to avoid this.

Yes, parchment paper will not affect the cookie.

Most stores carry it with the aluminum foil and wax paper.

Baking parchment is also called parchment paper and is available in most grocery stores. Parchment looks and feels like unwaxed wax paper.

Butter paper is parchment paper but in some countries they call it butter paper