Hi, just some elements, until someone knowing NMR better passes by...
"Parallel or antiparallel" is correct. That's a fundamental behaviour of electron or proton spin, which can't be stronger or weaker - it has two values only. What may be faster or slower is the frequency at which it precesses; this frequency depends on the magnetic field it feels.
At room temperature, man-made magnetic fields orient about 1ppm of all protons. That is, from 1,000,000 protons, you would have 500,000 up and as many down without a field (plus the statistical fluctuation of about 1,000 particles), and the man-made field changes this to mean 499,999 and 500,001. It's because the energy difference between up and down in the man-made field strength is much smaller than kT.
At relaxation, 1,000 particles still fluctuate, while 500,001 and 499,999 become again 500,000 and 500,000 - so 1,000,000 particles aren't enough to observe anything. It takes (much) more than 1012 particles to observe more signal than noise.
In NRM imagery (not analysis as far as I know), a field gradient changes the resonant frequency according to the position along one direction, and this gives resolution in one dimension, while a temporary gradient in an other direction can change the phase, and many different gradients permit a discrimination of the position by Fourier transformation. Is that what you mean?
Medical NMR uses dozens of varied pulse scenarios having different benefits, so one explanation won't cover them all. Beginning with NMR for chemical analysis is wise.