Maybe it's a stupid question but as the title says, in DC analysis how does the current from Vcc flows? Where is the - and the + of the voltage source? And how does the current flows in AC analysis when we also have Vi involved?
Whenever you see Vcc or +9V or any other voltage flag, it's really just a shortcut way of saying "this is a voltage source relative to ground." That means I can redraw your circuit as:
So the + side of the voltage source is connected to the "V" in your circuit, and the minus side is ground. Vi works the same way. That first capacitor will effectively be a short to AC (if the capacitor is large enough). So current will flow in from Vi in to the base of Q1, which will cause more current to flow through RC and the base of Q2, which will cause even more current to flow through RC and RE. It's a Darlington Pair circuit.