Yes, but the numbers 1A, 5V to 4V and 1 second in your example just don't live in the same space-time continuum together at the same time.

Yes they do.

The fundamental equation relating the voltage across and current through a capacitor is

I = C dV/dt.

This equation is the equivalent to Ohm's law for resistors. There is a similar relation for inductors:

V = L dI/dt.

If you let dV/dt = 1 V/s and C = 1 F then I = 1 A.

The current in my example is constant as the voltage on the cap changes. This make it valid to apply the above eqn. directly.

If a resistive load is used to discharge the cap, then the current will change as the voltage falls.

If you have a series RC circuit, the T = RC and 63% stuff can be derived from this equation combined with V= IR.

For a resistor in a series RC circuit you end up with

V(t) = Vo * (1 - e ^ (-t/RC)).

V(t) = Voltage on the capacitor as a fn. of time.

Vo = voltage source driving the R and C in series.

R,C = resistance and capacitance of the resistor and capacitor in series.

t = time (t = 0 is when the voltage source is applied to the circuit)

If you let t = RC you get

V(RC) = Vo * (1 - 0.367) = 0.632 Vo.