George..good questions.
First...if anybody reading, especially speaker re-cone folks, has any corrections to what I write, please jump in...this is all from memory, and I'm sure I've dropped a brain cell or two in the last 30 or so years.
Surround function:It's a spring, it has a K factor...X amount of force moves it Y distance in the linear range. As it reaches the limits of its travel, it takes more force to move it Y distance ie: the nonlinear range. Non-linear=distortion. However, we want it to go highly non-linear at some point so the coil doesn't crash into the back plate or jump out of the gap. The spider does that same thing, with the additional important function of holding the coil in the center of the gap. (The surround also does this but to a lesser extent) The surround and spider combine to determine the compliance, or spring factor of the speaker. There are many surround and spider configurations and materials to give the compliance and excursion desired. The compliance (spring factor) and the mass of the cone/coil assembly determine the free-air resonant frequency.
Surround treatment. There are many concoctions used for this, and for various functions. The simplest is in the case of a cloth surround when used in a reflex, closed or horn loaded configuration. It needs to be sealed with something to prevent air from blowing through it and leaking the air load designed into the enclosure. (Doesn't matter in open back cabs) They can be treated at the manufacturer (such as Hawley) or we could do it ourselves.
In the case of integral, or paper surrounds, there is a catch 22. The same paper we want to be rigid on the cone has to be springy (compliant) at the surround. There is an additional problem of standing waves, which is where frequencies with a wavelength smaller that the cone diameter (above piston range) travel from the coil through the cone and surround, bounce off the speaker basket rim, and back down the cone in a self-perpetuating cycle. Surround treatment, or doping helps control this. It changes the speed of sound through the paper at the surround, usually slowing it down. By adding a surface treatment, such as rubbery A400 or similar, it adds to the thickness of the surround, increasing the K factor, or stiffening the spring and raising resonant frequency. It also adds loss, or damping (like a shock absorber) to absorb standing waves. It also helps keep the paper from fatiguing and cracking. A400 is kind of like a diluted clear latex bathtub caulk.
To accomplish all of the above (damping etc), but lower the K factor and resonance frequency, another type of product is used (wish I could remember the product #), which soaks into the paper and softens it. You have probably seen this, because it remains sticky, and attracts dust. Think of it as a combination of WD40 and honey. It never fully dries.
Vented Pole Pieces. These are used to create airflow to cool the coil and gap. Yep...they can flutter. Ideally, the air flow is laminar...smooth and free of turbulence. At longer excursions ie lower frequencies, the air pocket contained under the dust cap gets compressed and decompressed to the point that it cannot flow smoothly through the vent. It becomes turbulent and tumbles, especially at the exit of the vent, where it abruptly changes pressure to whatever is outside the back of the speaker. Smack your palm on the end of a short pipe and you get the idea.
Solutions: One is to simply bore a bigger hole in the pole piece that can accommodate more air. However, at some point, you remove enough metal that you reduce the amount of flux the pole piece can deliver to the gap. The efficiency of the speaker drops and you are paying for magnet you aren't using. Another is to vent the dust cap or use a porous dust cap that can't build as much pressure under it. This can also be somewhat self-defeating in that it it creates a leak from the cabinet enclosure through the vent to the outside, plus reduces air flow through the vent, which was the idea in the first place. Sometimes you will see this in a speaker with a rigid dust cap with a hole in the center covered by cloth. Another elegant solution which I first saw on Hartley Peavy's Black Widow, was to taper the back of the vent so the transition to the outside was gradual..kind of like a little horn. I'm not sure if Peavy invented it, but it was a great idea and as far as I know, it worked. In my case on the SPL speakers, we had a big enough pole piece and a huge magnet wallop (96 oz). We simply increased the size of the vent until the flux dropped a bit in the gap, then backed off to the previous size vent. It worked and didn't flutter.
Hope this helps...Thanks...Rex