I have a quaud breaker, I have failed to find out why it was there as the wires coming from it were dead and the breaker was broken. My question is: The outside breakers of the quaud breaker are 15 amps, and I know I can use them as a circuit on each as is. The inside with bs bar are each 15 amp, can I use one side of the bus bar breaker as a stand alone 15 amp circuit?

Yes.
It can be 1 or 2 120 volt circuits(usually multicircuits). Also can be 1 240 volt circuit.