Reading recommendations to better understand how to understand the intended function of a circuit
I think any basic electronics book will get you to where you want to be, things like the art of electronics by Horowitz, Razavi or Sedra/Smith

to be honest though I think you can figure this out with a circuit simulator to get an intuition of what is going on.

what does a resistor do? remember ohm's law? if there is a current through a resistor, the shape of the voltage will be identical since V=IR where V is voltage, I is current and R is the resistance value.

the amplifier way of thinking... If you think of the transistor as an ideal switch controlled by voltage, any small current that the diode drives into the transistor is going to make the 26V from DC line be fully applied(or partly depending on saturation) onto the resistor.

I would not call it an amplifier myself since I don't understand what is the input to have a ratio, this is just me not understanding this particular circuit, not a concept issue.

To understand what your instructor meant, you need to understand Ohm's law, transistor operation, diode operation,  Kirchhoff's Voltage and current laws I would say.