Well, let see what the SRD has to say about the Air Elemental Whirlwind ability and see if we can find answers to your questions:
From the SRD:
Air Elemental
Air Mastery (Ex): Airborne creatures suffer a -1 penalty to attack and damage rolls against an air elemental.
Whirlwind (Su): The elemental can transform itself into a whirlwind once every 10 minutes and remain in that form for up to 1 round for every 2 HD it has. In this form, the elemental can move through the air or along a surface at its fly speed.
The whirlwind is 5 feet wide at the base, up to 30 feet wide at the top, and up to 50 feet tall, depending on the elemental’s size. The elemental controls the exact height, but it must be at least 10 feet.
Creatures one or more sizes smaller than the elemental might take damage when caught in the whirlwind (see the following table for details) and may be lifted into the air. An affected creature must succeed at a Reflex save when it comes into contact with the whirlwind or take the listed damage. It must also succeed at a second Reflex save or be picked up bodily and held suspended in the powerful winds, automatically taking the listed damage each round. A creature that can fly is allowed a Reflex save each round to escape the whirlwind. The creature still takes damage but can leave if the save is successful. The DC for saves against the whirlwind’s effects varies with the elemental’s size.
The elemental can eject any carried creatures whenever it wishes, depositing them wherever the whirlwind happens to be. A summoned elemental always ejects trapped creatures before returning to its home plane.
If the whirlwind’s base touches the ground, it creates a swirling cloud of debris. This cloud is centered on the elemental and has a diameter equal to half the whirlwind’s height. The cloud obscures all vision, including darkvision, beyond 5 feet. Creatures 5 feet away have one-half concealment, while those farther away have total concealment. Those caught in the cloud must succeed at a Concentration check to cast a spell (DC equal to the Reflex save DC).
Spectrum Rider said:
(1) Does the air elemental have to enter its opponent's space in order to catch him in the whirlwind? Does this provoke an attack of opportunity?
The SRD states that contact with the Whirlwind has to be made, so I would figure this means the whirlwind has to touch the character. Since it doesn't clarify it can use it's Slam attack, it would seem that it must move into a characters space (or if the character strikes at it). If it's on the ground, it can generate the debris cloud which gives Concealment (miss chance). So, it looks like it takes an AoO for it.
<edit - took out incorrect Flyby Attack AoO reference pointed out by Hyp. below>
Spectrum Rider said:
(2) Once it catches its opponent, can the elemental do anything other than whirl him around (causing damage, of course), or dropping him? Can it attack anything else while it has someone caught inside?
As I said before, I do not believe it can use the Slam attack while in Whirlwind form. The first round the character gets a Ref save to avoid damage the first round, then a second Ref save to avaoid being picked up. It automatically does the whirlwind damage 2d6 for Large Air Elemental each round the creature is caught in the Whirlwind.
Spectrum Rider said:
(3) Can it only have one opponent caught inside at a time?
From the plurals used in the writeup (can eject any carried creatures ), it would seem it can scoop up more than one, but I don't know an upper limit (you might use their STR to see what they could carry and how much they'd be encumbered by it and how their movement would be reduced for carrying a load).
Spectrum Rider said:
(4) Can it take a caught opponent up to an arbitrary height (at 100 ft. per round, you can get pretty high up) and just drop him? For non-flying creatures, this causes more damage than seems reasonable?
Yes it can do this. Realize that you would need at least a Large Elemental to scoop up a medium sized character (CR 5 for Large), and the right terrain to do this (like being outdoors, not inside or underground in a dungeon). Lots of damage? Yep.
Spectrum Rider said:
(4) What can the caught opponent do? Can it attack the air elemental holding it?
From what I see in the above, I don't think they can do anything unless they can fly (and thus can try to escape).
Spectrum Rider said:
(5) Can the caught character's allies attack the air elemental without harming the character?
I would say yes, the whirlwind on a Large Elemental would be big enough not to endager your friends (even with direct shot spells like Lightning Bolt). Elementals are dangerous enough to give the PC's the benefit of the doubt here.
Does any of this match with what you were thinking? The above is how I ran it when my PC got hit by a large one (luckily indoors). It scooped up the mage (who was blasting it), lifted him up 30' (max hallway height) and spit him out after two rounds. (2d6+2d6+3d6 for the fall = Ouch!). The mage hit the floor, cast Invisibilty and crawled away to hide with single digit hit points after that....
