How to replace an LED with a diode and stop LED after timer ends?
For the D5 question, you can simply remove it. It will not have any effect on the balance of the circuit.

The monostable mode of the 555 timer normally requires that the trigger pulse be shorter than the timer length. If not, the 555 stays triggered prolonging the length of the output pulse beyond the programmed time.

A simply fix for this is to change your circuit as follows:



(Image credit to tcrosley on StackExchange 180786)

Remove R9 and R10 in your circuit, add the components shown, and place the emitter and collector of Q2 in place of the SW1 switch shown.

Your timer will then run for the programmed length and not retrigger until your LUX sensor turns off and again turns on the transistor.