INCORRECT. Radio waves are not used to produce the MRI signal (see Hoult. The magnetic resonance myth of radio waves. Concepts in Magnetic Resonance 1989:1:1-5.). The MRI process relies purely on magnetic induction—magnetic fields oscillating at radio frequencies. (This does not mean that radio waves are not present.)
CORRECT. MRI images are made up of pixels (picture element), which correspond to voxels (volume of a pixel) in an image slice in the patient. Within a voxel (which may be a little cube of tissue), there may be many tissue types. The signal from each of these tissue types contributes to the average signal from that voxel. Even within a single tissue type within a voxel, there will be a small range of magnetic field strengths due to the varying proximity to other tissue types and the varying molecular environment of spins. As a result, we can only really classify spins as the same on a very small scale. In order to avoid difficult quantum mechanical concepts of the behaviour of individual spins, we can group them together by the magnetic field which they experience, and consider only the net magnetisation vector which results in a classical physical way. An ensemble of such spins is called a spin isochromat (which literally means "same colour"). There are many spin isochromats within each imaging voxel.
The precession of the net magnetisation vector of each spin isochromat will move in and out phase with other net magnetisation vectors (from other groups of spins) within the same image voxel. When these sub-voxel magnetisations precess out of phase, the overall signal from the voxel is lost because the oscillating magnetic fields produced all cancel out.
This is an important issue in MRI, because although spin isochromats can be set precessing in phase to start with, the natural dephasing of the net magnetisations within a voxel destroys the MRI signal. Signal measurement must take place before the magnetisation is dephased. Rephasing the MRI spins within a voxel for short time is part of the MRI signal acquisition process.
As a result of the varying magnetic fields experienced by spin isochromats, the Larmor frequency ω0 will vary throughout an imaged object (e.g. a patient). As well as the immediate enviroment of spins contributing to magnetic field variations, more variations are produced due to imperfections in the external magnetic field, and effects of magnetic field gradients which are used in spatial encoding. Note this—spatial encoding gradients, whilst helping to encode the signal across an image slice, actually contribute to destroying the MRI signal!