I wanna select the faces of the little band around the handle but for some reason when I try to select nothing happens. Not even in object mode I get the orange outline that's usually there. I've tried restarting the program few times but it didn't help.
You appear to have overlays turned off. This means that selected objects (and Faces, Vertices, etc) will not appear to be selected, because the blue/yellow/orange highlighting that indicates an object is selected is considered an overlay.
You can turn overlays back on by clicking the relevant button here: