Superconductors are strong diamagnetic in nature so if they are used as core of any coil do magnetic lines of forces pass through them – I mean inside them just as with a soft iron core?
Secondly if they are used as the coil wound on core then change in magnetic field induces current inside them. Does mutual inductance occur in them or not – because the magnetic lines of forces don't pass through them, or because they bend towards them?
As superconductors are perfectly diamagnetic, I would describe putting them in a transformer core as misuse, rather than use. They will do exactly what you don't want in a core material. Soft iron allows many times more flux for any given field than air, a superconductor allows zero flux, regardless of the field.
Superconducting windings, coils, behave just like ordinary windings, as far as having voltages induced on them due to changing magnetic flux linkage, and generating a field due to current flow through them, but without the \$I^2R\$ heat.
