Does the phrase at the beginning of the wielder's next [unstated type
of] action mean the affected weapon can be used to make iterative
By RAW, no, because "make an iterative attack" is not considered an action type. You'd likely be getting those from a full attack action, which is a full round action.
By that wording, if you had a way to throw it as a move or swift action, it'd come back in time to also use it for a standard action. Which is kind of silly, but welcome to RAW. You could house rule it such that you can use it during a full attack, but you'd almost certainly also want to do that with the Returning property if you do, otherwise the spell would be strictly better.
Does the phrase can be seized and thrown again mean the wielder
needn't employ a method of faster readying between iterative thrown
attacks (e.g. perhaps a crystal of return (least) (MIC 65) (300 gp; 0
lbs.), the feat Quick Draw (PH 98))?
Since you can't use it to make iterative attacks, it's a moot point. But assuming you could, the rules don't say. Returning is a free action to gab the weapon again (and says so), and in the absence of anything saying otherwise, I'd be inclined to treat this the same way.
Although the spell lacks the teleportation descriptor--therefore
presumably the weapon must reach the thrower manually (again,
presumably--although this goes unstated in the spell's description--by
flying (but burrowing would be hilarious))--is there a limit to the
distance the wielder can move between throwing the weapon and the
weapon's inevitable return?
No, because the spell doesn't say there is. That can also lead to goofy situations like the weapon going at warp 1 on it's way back to you, but hey. Magic doesn't obey the laws of physics, and the spell is explicit in when it returns to you. I do find it an odd omission, since Returning does say how it gets back to you.
As for the teleport subschool, it doesn't apply. That applies to spells that teleport something, which are conjuration spells. This is transmuting the weapon (hence transmutation school), and if it gave the weapon the ability to teleport back to you, that wouldn't necessarily need to have the teleport subschool. (It doesn't mean that it is teleporting or that it isn't teleporting, just that you can't rule it out by the lack of the subschool.)