Regarding gradients: The gradients used in MRI vary in *position*. Yes in time, as well, but only because they are pulsed. We can ignore ramping issues to first order. Since the field varies as a function of position, when you move around, indeed the flux is changing which can induce currents in looped conductors so as to oppose the change. This is called induction. Many people, my self included, notice a strange sensation when first entering an MRI magnet. This is because the field is only homogeneous over a relatively small volume, outside of which there are once again field gradients (these are different than the intentional field gradients used to obtain an MRI image). It is probably not axons but something in the ear that is picking this up, I am not sure. Also, field strength has *nothing* to do with this effect. It's how fast the field changes as a function of position, i.e. the gradient, combined with the velocity of the pickup object.
Regarding repulsion: Water is diamagnetic. That means that the little spins (i.e. electrons) orbiting the atoms of a water molecule tend to align *against* the applied field direction. These spins will experience a repulsive force, hence the levitation.
Large and costly magnets? Why don't we just start levitating things at the LHC?
magnets aren't nearly strong enough, that's why