Velleman Sound to Light Kit Questions
What is the purpose of the C4 capacitor? Is this what it's known as the bulk or smoothing capacitor? What is the purpose of resistor R8? It looks like its on a weird place being in series between the power supply positive lead and and half of the circuit, what is up with that?


As @respawnedFluff explained, its likely a simple RC filter.


  Why does't the T3 transistor have a resistor on the emitter leg? Don't you need that resistor (for negative feedback) to be able to stabilize the transistor such as preventing thermal overrun, minimize beta variations effects between transistors etc?


No. T3 is acting as a simple Emitter-Follower Switch. It's purpose is to switch T4 On and Off only.


  What is the point of having R12 and R5 as two separate resistors? Can't those two resistor be replace with a single resistor and achieve the same affect?


Not for the intended purpose. R12 is a weak pull-up designed to keep T4 biased to V+, while R5 is a strong pull-down resistor for T4. When T3 is on, T4 is turned on via R5, overriding R12. Otherwise T4's base would be left floating when T3 is turned off.


  Why aren't the biasing resistors (voltage dividers) on T1 and T2 not identical? Its the exact same transistor so why is the voltage divider biasing different (specifically on R2 and R10)?


T1 and T2 are both set up as amplifiers. T1 is a pre-amp boosting the small changes from the mic, while T2 is a second stage amp. Hence the different gain values used. They likely found these values the best for their kit. As @RF commented, they can have the same gain in some situations.