2.  Yes, you have to build it.  When you push the plunger of the push button, the cap fills.  Then when you disconnect from the voltage by releasing the plunger, the cap acts like a reservoir.  What happens to the brightness of the LED as the cap drains?  I can't tell you everything.

3.  a.
     b.
     c.  The cap should measure close to full voltage. 
     d.  The LED should light and go dim, just as if the PB had just been pushed & released. 

4. a)

 

4. b) Less capacitance => Less energy stored

5.  Capacitors store electrical potential (voltage and current)

6.  The LED fades when you push and hold the plunger.  The action here is opposite that of the PBNO.