Hi,
I forgot my nodal analysis learnt during 1st year, but I can give you some light on the 100 ohms varying resistor.
Whether the varying resistor is 100 ohms or 1kohms is of no concern in the amplifier circuit because it effectively acts as a potentiometer OR potential divider. Whatever the
voltage at node 2 depends on the position of the dial: If it is at node 3, the voltage at node 2 is the full 5V : If it is at node 1, the voltage at node 2 is the full 0V : If it is halfway in between, it is 1/2 * 5V = 2.5 V.
This is because as you turn the dial downwards, the resistance with respect to node 1 decreases, and the resistance with respect to node 3 increases.
The voltage at node 2 can be found using the potential divider formula:
R1/(R1+R2) * Vcc.