With capicitors, it isnt physical size that matters. What you're saying though is true,capacitance is the amount of charge required to increase the p.d. across the terminals. So yea, "bigger" = longer.
No, if you charge it with 1.5V, it will discharge from 1.5V. I could give you a huge analogy to explain like my physics teacher did but it would take too long on a forum though. The current around the circuit decreases exponentially as the capacitor discharges.