Christy, let me share with you part of the problem you will face trying to read the output(s) of the CD4020.
The way the circuit is supposed to work is that clock pulses enter the 4020 on pin 10 the clock in. The counter is advanced one count on the negative transition of each incoming clock pulse. The counter is reset to the zero state by a logical “1” at the reset input pin 11independent of clock. (Note in the drawing the counter reset is tied to logic high so won't count but anyway moving along). All the counter knows is that it counting pulses it has no clue what they mean, it has no regard to time. Hold that thought.
In this case they try for a clock of .21 seconds and if we do the math for the clock circuit (which as AudioGuru points out is a lousy clock) it would be .207 second but I guess we can say .21 second as it is close enough for this. So lets move along to actual time in hours. We know there are 60 seconds to a minute and 30 min = 1/2 hour. Therefore 1/2 hour of time = 1,800 seconds. Since our clock pulses are .21 seconds it will take 1,800 / .21 = 8,571.43 pulses for 30 min. Forget the .43 but we still have 8,571 pulses to make our 30 min. If you wanted to display this numerically on a display first it would not be easy and second the numbers seen would not mean much.
Now if you look at T1, T2, and T3 in the circuit. For the buzzer to beep they all must be on and in saturation acting as a switch. (Note: I see 22 KΩ base resistors, I believe that is also wrong, I believe 2.2KΩ would be about right). All three of those transistors, to be turned on need the logic out on Q1, Q5 and Q14 to be logic high. Now you figure out the bit count. Think powers of two and bit weight. All the buzzer will do is a beep when all of those bits are logic high. As soon as any one of them goes low in the count the beep stops. Eventually Q8 and Q14 will hit a high on both bits. When N3 pins 8 & 9 are high pin 10 is low. That low is applied to pins 12 & 13 of N4 making its output pin 11 high and turning on T4 which should in turn allow RL1 to energize. We already covered the disaster at the normally closed contacts of RL1 and mains voltage.
Now if you want to get started with timer and counter circuits I would suggest you start with more simple circuits using binary counter dividers and gain an understanding of simple binary outputs. Chips like the 74192 nd 74193 come to mind or their CMOS brothers. Start simple with 1, 2, 4, 8 and then move along.
You can ask your question(s) in other forums but I believe you will get the same answers.
Ron