LED doesn't register as LOW after a switch has cut all power to it
The diagram is open to several different interpretations, depending on what's inside the four-terminal switch.  On many such SPST switches, two adjacent terminals are connected to each other inside it, and the other two likewise.  Which are which in the diagram isn't indicated.

That aside, what is clear from the diagram is that pin 2 is connected by wires to +5V, and will always read in as high.



Edit 1:
The schematic [posted later] is unclear.  It should be arranged so that solid lines represent wires or pins, with solid lines between things that are connected.  Place items in the drawing to reduce unnecessary and confusing crossing lines.  For example, supposing that the dashed line from pin 2 of R1 represents a wire between pin 2 of R1 and pin 2 of LED1, it is unclear whether the wire bends around the top right pin of S1 (can't read number) or connects with that pin on its way to LED1.  For another example, nothing is shown connecting to pin 1 of R1, and only one long dashed line connects the R1/S1/LED1 group to the Uno.