transistors - S8050 D331 base resistor calculation

I was trying a basic transistor circuit to understand transistors (LED on the collector without a base limiting resistor ).

Now on to the next step, to know where and when to put what values of resistors so that the photoresistor and S8050 D331 transistor I have together work as a dark detector.

I need to explain to myself why the circuit does not work if the photoresistor or the load or the extra base resistor are not in their exact positions.

I was referring to http://www.petervis.com/GCSE_Design_and_Technology_Electronic_Products/Transistor_Bias_Calculator/Transistor_Bias_Calculator.html and i have trouble finding the values and calculating them.

Q1: is this the only way to go about it? Suppose a middle school kid is doing this for a science project, how does the kid understand which resistor to put where?

Q2: Assuming this is the only way - for S8050 D331. How do I decipher which values to use in the calculator above? http://alltransistors.com/transistor.php?transistor=52916

^{simulate this circuit – Schematic created using CircuitLab}

The resistance of photoresistor is unknown (am using a snap circuits kit - part 6SCRP).

Q3: If i move the photoresistor to the left of the voltage divider and the 5.1K resistor to the right, OR if i put the load on collector the circuit does not work. It works perfectly when the potentiometer is at one of the extremes (I guess it is high).

I want to understand with calculations, how things work.