About the NPN Transistor
The NPN transistor has three prongs- with the flat side facing towards you, they're called (from left to right) the emitter, base, and collector.
The collector is connected to the positive battery wire in most cases, and the base acts like a switch to the emitter. If the base is powered, then the emitter will, true to it's name, emit voltage.
How does the circuit work?
The red wire is connected to the resistor. The resistor is connected to the positive end of the LED. The negative end of the LED is connected to the yellow wire, which is connected to the black wire, which is connected to the battery. That makes a circuit.
Sharing Current Explained
When current is shared, all segments light up but they are more dim than when just one segment is plugged in.
How does the IR LED and phototransistor circuit work?
The power goes through the red wire and resistor and powers the IR LED. In a separate circuit the power goes through the resistor through the phototransistor through the yellow wire to the visible light LED and back to the battery.
What does the voltage regulator do?
The voltage regulator drops the circuit voltage to 5V by dispersing 4V directly to the black battery wire to not fry the chip.
How does the reed switch work
The reed switch has two pieces of metal inside that are open. When activated by a magnetic field they close completing the circuit.