the details are on page 3 in the paper.
for (c), the oscillator is free running, meaning no one is controlling it. the output of the osc is used as both the trigger and input of the oscilloscope (with internal delay between these two so one can sample the other).
I do not quite get your second question. but (a) seems only shows the histogram result and you can derive the variation from it; (e) provide more instrument that you can see the variation relationship to the loop bandwidth (which can be used in design implementation?)