Does electric field generated by changing magnetic flux generate an opposing magnetic field?
Edit:  WARNING: Some of my descriptions may be false.

Induced current creates a magnetic field that is opposite to the one that created it. This is the reason why the magnetic field magnitude decreases when it flies trough the conductor. It will decrease according to how easily the eddy currents can be induced inside a material. If the material is non-conductive, eddy currents will not be created and hence the magnetic field will just "fly" trough.

If you used a super conductor, because it has no resistance, it will create electrical current based on the whole magnetic field strength. Because of this, this current will produce exactly the same magnitude of the opposite magnetic field which will cancel out the magnetic field. This is also the reason why magnetic fields can't penetrate the super conductor and is a perfect shield. It also gives rise to the "levitation effect".

To the second part of your question:
The changing magnetic field will indeed create an electromotive force around that invisible loop, but if no current is flowing, opposing magnetic field WILL NOT be created. This is the reason why the magnetic field isn't being "consumed" but will radiate outwards indefinetely or untill getting into contact with some electricaly charged particles.