For question number five, the answer is it depends on the type of superconductor. For type I superconductors, the superconducting carriers are ideally only running along the surface of the material in a layer called the London penetration depth. For type II superconductors, the carriers start on the surface, but can ultimately use the entire volume. There's a mathematically accurate model of this called Bean's model. Basically as each layer of the superconductor hits reaches its critical field, (or critical current), the next layer begins carrying current. The diagram1 below describes the model briefly.
References
1. Bean, C., "Magnetization of High-Field Superconductors", Rev. Mod. Phys., 36, (1964), 31
My conclusion is therefor: There would never be induced any current at
all. Current can never be induced in a superconductor loop. Is this
the case or am I misunderstanding my book?
One cannot conclude this for the reasons you have given; it does not follow from the fact that the total flux does not change that the current cannot change.
For a non-zero, finite resistance, there must be an emf to sustain a circulating current. However, for the case of zero resistance, there can be a current without emf (zero resistance) and further, a changing current.
Since the net flux through the surface bounded by the superconducting loop is just the magnetic flux due to the magnet plus the magnetic flux due to the current through the superconductor,
$$\Phi = \Phi_m + \Phi_i$$
imposing the condition
$$\frac{d\Phi}{dt} = 0$$
implies that
$$\frac{d\Phi_m}{dt} = -\frac{d\Phi_i}{dt} $$
Thus, if the magnet is moved, causing $\frac{d\Phi_m}{dt} \ne 0$ then, it must be the case that $\frac{d\Phi_i}{dt} \ne 0$, i.e., that the current circulating through the superconductor is changing.
Since the net flux is not changing, there is no emf around the loop enclosing the surface. Nonetheless, since the resistance is zero, the current is independent of the emf and so one cannot conclude that the current is zero or unchanging.
Best Answer
Actually, induction works, although it is often used a bit differently than you described. You can place a warm superconductor loop into a normal coil. As you switch the coil on, there will be some current inside the superconductor, but since it is not cold yet, this current quickly dies down. Then you cool the superconductor below its critical temperature. When you now switch off the normal coil, the flux-change induces a current in the superconducting loop. This current is there to stay.
With the proper coil windings, you can get quite large currents, but you won't be able to get to field energies that are needed in NMR or MRI machines. These magnets are energized (sometimes called "charged") differently. The trick is to make part of the loop normal conducting during charging, and then "close the loop" when the coil is energized.
If you want to know details, this is the electrical schematic on how it is done:
I used values from a typical 5 Tesla NMR magnet that I energized a few years ago.
I will leave out all those pesky details that make charging a real superconducting magnet a hassle. The procedure boils down to this:
With the loop closed, the magnet is now in "persist" mode, so the current goes on forever. Well, not quite forever, there usually is a little bit of resistance that leads to "flux creep". For the magnet I am using this is an unusually low value of $10^{-11}$ Ohm, which makes the current decay with a time constant of a few 100 000 years. The designer of the magnet speculates that this resistance is caused by the weld that is needed to turn the wire into a loop (see the link above, near the end of the paper). Other reasons that are often given for this effect involve details that are specific to type-II superconductors.