As Dr_Doggy said, look at pin 6 relative to ground. 2/3 Vcc is the magic number. @ 9V, this is 6V.
With light on the photocell, pin 6 relative to ground has to be below 2/3 Vcc. The photocell and R2 divide the battery voltage.
Instead of looking at formulas, let's look at basics . The current through R3 and R2 is I=Vcc/(R2+R3). The voltage cross R2 is I*R2 and the voltage across R3 is I*R3.
The part acts as a comparitor, latch and driver in this application. Datasheet:
https://www.ti.com/lit/ds/symlink/lm555.pdf
Magic numbers are 1/3 and 2/3 Vcc for this part.
Piezo buzzers can be troublesome. You could have bought a piezo transducer or speaker, They wont work. There is a polarity for buzzers. make sure the buzzer works when directly connected to the battery.
PS: Relative to ground means black connected to negative. We will also assume the meter can display polarity for future reference. Ground of the (-) supply is USUSLLY the referenec in a circuit with a single supply (9V battery). Most voltages are measured with respect to a reference. Occasionally, you lokk at voltages across things.
You mentioned that you got No resistance across resistors. There is a lot of problems with no. Use low or ~zero, but not NO. "No resistance" can easily mean infinate. Modern meters are such that they don't turn on semiconductor junctions, but they can.
Make sure your meter reads close to zero when the leads are shorted. Leads have resistance, Might be as high as 0.5 ohms.
Watch your probes. Some that are really sharp actually have an insulator along most of it's length.
generally you have COM, (Volts/ohms), and a mA Jack. Since measuring current is almost like putting a direct short (low value resistor) across what your measuring, the current scale is protected by a fuse in a good meter. You also use different connections,
Ohms and volts use the same terminals, but measuring ohms in a powered circuit can destroy the meter. Capacitors have charge, so discharging them is a good idea.
Probe leads break or degrade when their muti-stranded wires break.
Probe leads have insulation ratings. When you have a chance loot at the CAT ratings of meters.
This stuff applies to most DVM's. High voltage, High frequency and extremely low currents like in nA, pA or fA ranges require much different rules.
Any meter disturbs the measurement. Most (not all) meters are designed for a 10 M (10,000,000 ohms) ohm input impeadance. Thus measuring anything is adding a 10 M resistor, thus measuring the voltage across the 10M cell will disturb it. It makes it now look like 5 M.
The formula for resistors in parallel is 1/Rt=1/r1+1/r2+....1/Rn
12k in parallel with 10M is is close to 11859. The percent error is close to 1% if measuring voltages. Tolerances already exist in the part values and with temperature primarily.
Measuring current can also add a resistor in series.
This blurb is not all inclusive.
Furthermore, you may have to out a tube around the photocell to take out ambient light.
This circuit is not really a good application. It will be dependent on stray light. Remote controls modulate their output, so the IR from the sun or lamps don't confuse it. A beam break detector over large distances for an IR LED should be modulated so ambient light is rejected.
So, the voltage across R2 is easier to measure. Compute the voltage across R3 as battery-R2