[morzh]

I doubt you need to know the exact value of the inductor.
Suffices it to know, it is big and in 10s of H.

0.05uF cap is there to try to compensate for the ripple voltage.
The idea is, I think, that if there is a ripple via the inductance, and the current lags the voltage by 90 degrees, then that ripple could be nullified by parallelling a capacitor that would provide the same size ripple current which leads the same voltage by 90 degrees. The resulting phase shift between the AC component of the currents (ripple current via inductance and the current via the cap) is 180 degrees.
Of course the shape of the current through the inductor is not exactly the same as it is via the cap. So they will not totally compensate each other.

Picking the cap depends on the load. With the load current of a certain size the ripple voltage is Iripple*Rload.
You could watch this on a scope.
Then knowing the voltage you could keep inserting the caps until you see the optimal reduiction.

Or if you want to be a bit more scientific and calculating, measure both load current and the load voltage, calculate the impedance, and solve for the capacirtive impedance so the divider between the cap and the load gives you the same amplitude of the voltage as the ripple AC component given the AC ripple before the choke.
I would do the former as it is easy enough.