Yes the BJTs are configured as an amplifier. Think about what happens to the collector voltage on Q1 when the base voltage changes, note that it's connected to the base of Q2 and do the same there. Then think about what happens to the collector voltage, when the voltage at the emitter of Q2 changes. Hopefully you'll see that the emitter resistors and R25 provide negative feedback, which reduces the gain but brings about many advantages: look them up.
The 74HC02 is configured as a flip-flop. notice how it's drawn as AND gates with circles on the inputs? The circles denote that there's an inverter before each input. Look up DeMorgan's theorem and you'll find they're NOR gates.
Did the kit come with source code for the MCU? If not then it's not very good. The whole point of building a kit is to learn how it works!