How to calculate ripple voltage in this bridge-rectified zener-regulated circuit?
You can pick R1 to produce an average current of Iz (from the zener datasheet). While you are there, look up the zener impedance at that current. You can think of the zener as an ideal voltage source with a resistor in series. The value of that resistor is highly dependent on the zener current, of course. 

Calculate the ripple voltage at the capacitor from the current from the capacitor (assume it is constant and equal to (Vp-Vz)/R1. Symbolically (as a function of C). 

Calculate the ripple voltage across the zener from the zener impedance, ripple voltage and source impedance (R1 || 50K which you may be able to say ~= R1). Again, as a function of C.

Find the minimum capacitor value to yield 1% ripple. 

You can calculate the load regulation similarly. 

Here's part of a table from a zener datasheet: 



There are two currents at which the zener impedance is specified, but the zener voltage is only specified at Iz.