The best way to troubleshoot that circuit is with an Oscilloscope, but I've guessing you don't have one.
I have a scope on my bench! An Rigol MSO5074. It has four channels and all my probes are set at 10x attenuation. What points of interest should I look at?
Using only one probe, connect the ground clip to the negative terminal of the 9v battery (marked "2" on your schematic).
With the LDR illuminated, look at Q5 collector with your 'scope set to DC coupling---note if the voltage is around +9v(high) or very much lower.(low).
If Q5 is an NPN transistor as drawn, with the LDR in its low resistance condition, Q5 should be turned off, with its collector "high".
Following the schematic, if Q5 collector is "high", Q1 base should also be "high", turning that transistor on.
Now remove the illumination of the LDR----rechecking Q5 collector, it should be "low", as should be Q1 base.
This will prove out the operation of the LDR & Q5 circuitry.
You can now follow the schematic through the monostable, but I would suggest now going to the emitter of Q6.
If your mono is working, Q6 emitter should go "low" when you remove the light from the LDR, turning that transistor on & making the alarm sound.
After some time, the mono should time out, taking Q6 emitter high & turning the transistor & alarm off.
From my reading of the schematic, the astable should be continuously running, so you should see its output appearing at Q6 base.
It is incredibly tiresome writing (& no doubt reading) these troubleshooting steps, whereas if I were standing alongside you in your lab, they would be but a matter of seconds.
I also know that there are always "vultures" waiting to pick such dissertations to pieces!