My copy of The Book is currently on its holidays, touring Australia and New Zealand with one of my colleagues. But to answer (hopefully) your first question...
The physical meaning of an end correction is that pipes don't behave ideally. If you measure the first resonant frequency, you'll find that its corresponding (half) wavelength is a bit longer than the pipe. The actual standing wave protrudes from the ends of the pipe by a little bit - the end correction. Not really surprising, because some of the atmosphere at each end will be influenced by what's going on inside the pipe. And the degree of influence depends on the form of the ends of the pipe.
For a Helmholz resonator, the "length" of the neck should include the end corrections at each end, because it is the effective length of the column of air making the "mass" part of the equivalent spring-mass system.
In practice because this end correction is an imprecise amount, the acoustic length is also imprecisely defined and leads to a "squashing" of the TL curve of the resonator (lower, wider resonant peak). Reducing the length of the neck magnifies this effect, because it increases the uncertainty in the acoustic length. Long, thin necks give sharp, high peaks. Short, fat necks (of equal volume) give rounded, low peaks.
The same may be true for 1/4 wave resonators, for the same reasons.
I don't know the answer to your second question. You could try looking into "Noise and Vibration Control" by L.L.Beranek
