I don't really follow your question 2. One problem is your diagram. Try to learn to draw standard schematics rather than the physical layout on a breadboard. It is much easier for other people to follow.
From what I can gather, Q2 is being used as an oscillator. It generates a small oscillating signal that provides the AC signal. Q2, the 2N2222 transistor is being used as an amplifier, to provide enough drive current to make an appreciable sound. Without the amplifier, I guess the 2N6027 can't provide enough current to drive the speaker, at least with the components shown.
Capacitors can ideally provide infinite current when shorted, but only for zero attoseconds. They have a finite amount of energy stored, you can discharge it as fast or as slow as you want (in reality of course there are limits on both ends). Ultimately, your power has to come through from the power supply. In this case, the capacitors job I think is actually to set the oscillation frequency, it isn't really a energy storage device, although of course it naturally stores energy as part of its job. If you change the resistor and capacitor values together you can probably change the maximum power output of the 2N6027, but I would guess that it can't handle enough to drive the speaker by itself, hence the presence of the 2N2222 as an amplifier.