Inductance

Inductance is the ratio $L = N\Phi_B/I$, and like capacitance it is fixed by geometry: for a long solenoid $L = \mu_0 n^2 A\ell$, with the current cancelled out of the derivation. Mutual inductance $M = N_2\Phi_{21}/I_1$ is the same kind of ratio between two coils. The voltage across an inductor is $V_L = L\,dI/dt$: zero at steady current, opposing a rise, driving a fall, and sustained by the changing flux rather than by any resistance, so a superconducting coil can hold volts across it. Raising the current banks $\tfrac12 LI^2$ in the field, at a density $B^2/2\mu_0$.

Three errors account for most of the trouble. Treating the inductor as something that opposes current, so a steady current is expected to drop a voltage or slowly die, and a decreasing current is expected to meet no resistance at all. Refusing a zero-resistance coil any voltage because $V = IR$ gives zero, which deletes the $L\,dI/dt$ term and makes every LR loop equation fail to balance. And letting $L$ grow with the current because the flux grew, when the flux grew because the current did and the ratio never moved.