I want to scale the individual pieces down, but if I try so simple scale them with s then the whole object is scaling down. Can I scale them individually?
Currently you ARE scaling them all individually, but you have selected nearly all the vertices so the effect is the same as scaling the object. Assuming the attached pic is more or less what you are after, you will need to add more geometry.
Set your pivot centre to individual origins (red arrow), select the faces, hit E to extrude then S immediately to scale. If you don’t want to scale on Z then also immediately hit Shift-Z after the S.