Transmission Line Question
The easiest way is to use any Spice simulator. It has "ideal transmission line" element. You can learn everything about this circuit using "frequency domain analysis".

Alternatively, you need to count for reactive impedance of the capacitor (1/(i*2*pifC)). There are two waves for each frequency: one running from the source to the load and another one running opposite direction. Make the amplitude and phase of the second (opposite) way variables and solve for correct voltage and current on the reactive load.