I'm unfamiliar with the geomagnetic implications, so I'll focus on your first question. Perhaps if you link to specific studies concerning induced magnetism in the Earth, I can say something about this aspect.
A surprising amount of materials contain more or less localized magnetic moments on the atomic scale. However, the interactions between these moments is usually such that the low-temperature, magnetically ordered state of these systems doesn't show a net magnetic moment. You will only be able to see a large (remanent) magnetization ("a magnet", one that you can stick on your fridge) if the atomic moments in the material prefer to align in the same direction. These materials are called ferromagnets. Other materials prefer to have an antiparallel orientation (as much as possible) of neighbouring local moments; these are called antiferromagnets. And then there are entire classes of materials which show complex magnetic structures at sufficiently low temperatures, and more.
Now, what makes a ferromagnet is that at sufficiently low temperature (the scale of which is defined by the magnitude of the magnetic interactions that try to order the magnetic moments parallel to one another) the atomic magnetic moments order, and a macroscopic magnetic moment appears spontaneously, without the need for external magnetic fields. If you heat up a ferromagnet, its magnetization will decrease, and the net magnetization ultimately vanishes at (by definition) the Curie point. The trick is that this phase transition (from ferromagnetic to paramagnetic phase) is not because the local magnetic moments were to disappear, but rather because the moments are no longer ordered at the given temperature (thermodynamically speaking, the magnetic interaction is no longer enough to beat the free energy gain available through increasing the entropy). You can increase the temperature further to kill the local moments themselves, but there's quite a large region of paramagnetism in between (in iron the Curie temperature is at 1043 K, while the local moments disappear at the Stoner temperature of around 6000 K)
These all imply that above the Curie point you still have a paramagnet: a collection of disordered local magnetic moments. Introducing an external magnetic field will then induce a net magnetization. What's important to keep in mind is that temperature is crucial, and the magnetic response you see will depend on the magnitude of the ferromagnetic interaction (trying to order the spins parallel to one another), the external field (trying to order the spins parallel to itself) and the temperature (trying to disorder the spins).
One of the characteristic quantities of magnetic materials is the magnetic susceptibility which tells you how strong a system's magnetic response is to an external magnetic field. Above the Curie temperature (i.e. in the paramagnetic phase) ferromagnetic materials more or less follow the Curie–Weiss law. This implies two things: firstly, that the induced magnetization of such a paramagnet decreases with (some power of) the reciprocal of the temperature; and secondly, that as we approach the critical temperature (coming from the high-temperature phase) the susceptibility diverges, which means that the system reacts very strongly to external fields (it becomes gradually infinitely easy to induce a net magnetization in the system just above the Curie temperature). But due to the fact that the local moments are disordered above the Curie temperature and ordered below, the magnetization of the material in the same magnetic field can show huge difference between the ferromagnetic and the paramagnetic phases (although I don't have any factual evidence to make a more quantitative statement).
tl;dr in ferromagnets (systems with spontaneous net magnetization at low temperature) there is indeed room for induced (i.e. non-permanent) magnetization above the Curie point, although this magnetization will be smaller and smaller as the temperature is increased (assuming constant magnetic field). At sufficiently high temperature even the local moments disappear, and the material becomes non-magnetic, but this typically happens at much higher temperatures.
