Can someone please show me how these circuits would look in LTspice? Can you also point out where I need to probe?
For the first question they have given clear instruction to use 3 diodes in series to represent a red LED and 1048 resistor to represent 1k resistor with 5% tolerance. Connect these and increase the input voltage in steps of 1.5V. Observe the voltage across the diodes and current through the diodes (of course it is single loop, current will be same in the circuit) at each increment. Plot the v-i characteristics. 

I have simulated this in PSpice using DC sweep analysis. The v-i plot across the diodes should look like general v-i characteristics of a diode as shown in the following graph.

Try to do the same experiment with components on a board with all the other known parameters and compare the results. 

For the second question you don't need to simulate to get the resistor values. You have 2 required variables, 2 unknown variables and 2 equations. You should be able to solve the equations. Keep in mind if you get non standard resistor values, either you can achieve the resistance using resistor combination or if you want to be cost effective take nearest standard resistor values and recalculate the duty cycle and frequency.