Formation of Net Magnetisation
INCORRECT. The idea that spins move like a compass needle under the influence of an external magnetic field is a limited one. For example, how do spins "point South" (align against the field direction)? This might be considered a higher energy equilibrium state for a compass needle, but it is unstable. Furthermore, why would only a very few extra spins align with the field in the lower energy, stable state ("pointing North")?
A consistent classical description does not need the alignment of spins fully with, or fully against the external magnetic field direction. The "parallel" and "antiparallel" states which are often used to describe nuclear magnetic moments is helpful, but only as a description of the equivalent number of particles in these orientations which would produce the correct net magnetisation vector. (Even in the classical description, spins do not align exclusively parallel and antiparallel to the external field.)
If the classical description is used—with the simplification of allowing spins to reside only parallel and antiparallel with the external magnetic field—the Boltzmann distribution may be used to calculate the proportion of spins in the higher energy state due to thermal energy (the number of spins in each state is almost equal).
This is a confusing topic; unfortunately most textbooks mix the classical and quantum mechanical explanations of MRI. Try again.
INCORRECT. This answer is a mix of the quantum mechanical (QM) and classical (CM) descriptions of MRI. For example, QM does not limit spins to only two states (spins are actually in superpositions of two eigenstates). CM does not limit spins to only two states either, although sometimes only two states are used as a simplification, from which correct calculations may be made. For example, we can then easily imagine opposing spins "cancelling out". (See also the response to the first option on this page.)
Microscopic fluctuating magnetic field
CORRECT. Thermal energy of the parent molecule (e.g. H2O) manifests in vigorous molecular tumbling, and collisions with other molecules. The protons of interest in MRI (hydrogen nuclei in water and fat molecules, mainly) are almost oblivious to this—their nuclear magnetisations continue to point in the same direction in space in spite of rotations or collisions of the parent molecule. However, a very slight change in the magnetic field experienced by a nuclear spin is caused by this turbulent molecular environment. The magnetic field fluctuates slightly in magnitude and direction, and the angle of precession wanders very slowly (slowly compared to the timescale of the precessional motion which is a few nanoseconds).
Formation of M
It is slightly more probable that a nuclear spin will "wander" towards an orientation with a lower magnetic energy than an orientation with a higher magnetic energy. Over time (up to seconds) a net magnetisation forms. This stable anisotropic distribution of spins which forms when a sample is placed in a magnetic field is called thermal equilibrium. Though this state is stable, it is not static. Spins precess and "wander" continuously, but the net distribution of spin magnetisation remains the same.
The net magnetisation vector has orthogonal components Mx=0, My=0 and finite Mz (the net magnetisation vector M does not precess because the precessions of individual spins are out of phase, and all Mx and My components are cancelled).
This net magnetisation vector is manipulated in MRI, and consideration of individual nuclei pointing this way or that is abandoned.
Further reading on this topic:
Books: Spin Dynamics p32