OK, last question first. With the exception of small amounts of leakage, the current returning to the power supply in your typical 2-wire circuit will be equal to the current leaving the power supply. If the difference between the current leaving and returning through the current transformer of the GFCI exceeds 5mA, the solid-state circuitry opens the switching contacts and de-energizes the circuit.
If the GFCI is tripping, you're leaking current somewhere. If the test button on your GFCI trips the breaker, and you can reset it, your breaker is probably OK. As far as disconnecting the load and still not getting any power at the GFCI receptacle, I'm not sure. I have never tried that before, but it does not surprise me if it does not work.
Breakers usually work for long periods of time with no issues. I think it would be highly unlikely that both breakers failed at the same time.