The interaction between the string and magnet (and it’s relationship with distance is complex. The general answers to your mind are:
a) usually
b) no, precision is not a factor
The pickup generates sound by the metal string moving through the magnetic field and inducing a current in the coil. The closer the pickup to the string, up until a point, the stronger this effect will be.
However, when the distance becomes too small, a few things happen. The timbre changes to be less distinct and more muddy as the dynamic range of the generated signal is compressed. Sustain also decreases. Both of these are likely because the magnetic field is now strong enough to have a physical dampening effect on the string that appears as tonal changes.
The DiMarzio Model P has a very strong ceramic magnet. This is where much of its character comes from.
@terb nailed the finer points if adjusting there - the top of the pup shpuld NOT be flat from E-G but should instead follow the radius