Purity Judgement
I read the effect as-written as:
All allies within 30 feet choose an ongoing effect which is affecting them; they may attempt to save (with a +2 sacred bonus) against that effect (even if it normally does not allow a second save), using the effect's original save DC. Success either counts as a success towards removing the effect (for poisons and such) or removes the effect; failure has no ill effects (eg., if you're poisoned and fail this save, you don't take the poison's damage).
The revision in your question is slightly more powerful, if only because it raises the possibility that a dead character (eg., who has failed a save against the Poison option of Prismatic Spray) could make a save and actually not have died.
Justice Judgement
I think that the effect is pretty plain: for one round per caster level, all creatures within 30 feet of the caster, which are either affected by Invisibility or actively using Stealth, are limned; this causes them to suffer a -20 penalty to their Stealth checks. This nicely removes the +20 bonus that immobile, invisible creatures get to their Stealth. So, a creature can still try to hide, but they're going to have a hard time of it. I don't see an Invisibility Purge in there, but a -20 to Stealth is only very slightly different.
Yes
Because as long as the effect has a duration and is magical, it will stop working inside an antimagic zone. And once you walk out of it (or the zone walks away) the magical effects return.
Antimagic does not dispel magic; it suppresses it. Once a magical effect is no longer affected by the antimagic (the antimagic fades, the center of the effect moves away, and so on), the magic returns. Spells that still have part of their duration left begin functioning again, magic items are once again useful, and so forth.
Some spell effects, like flesh to stone, have no duration, are instantaneous effects (see bellow), which are not subject to antimagic zone because the spell already happened and what remains is the result of the spell.
The "stone" is not magical, its real.
Another example is the damage caused by a Fireball. The spell itself wouldnt work inside an antimagic zone, but the damage caused is instantaneous, once the spell is cast and the damage is taken, the remaining effects (health lost, burn wounds, ego hurt, etc) are not magical per se.
Shapechanging in general mimic the spells from the polymorph school, which do have a duration.
Timed Durations
Many durations are measured in rounds, minutes, hours, or other increments. When the time is up, the magic goes away and the spell ends. If a spell's duration is variable, the duration is rolled secretly so the caster doesn't know how long the spell will last.
Change Shape (From universal monster rules) says: This ability functions as a Polymorph spell, which has Duration 1 min/level (D).
But Change Shape specifically clears it up that the creature can remain in that form indefinitely unless said otherwise. Meaning that it has a long-lasting duration.
Instantaneous
The spell energy comes and goes the instant the spell is cast, though the consequences might be long-lasting.
Called creatures won't get dispelled either, because the spell that bought them to the material plane already did it's work, the creature is physically here and won't disapear in an antimagic zone. But a summoned creature will disapear as long as it remains "inside" the zone.
Calling: a calling spell transports a creature from another plane to the plane you are on. The spell grants the creature the one-time ability to return to its plane of origin, although the spell may limit the circumstances under which this is possible. Creatures who are called actually die when they are killed; they do not disappear and reform, as do those brought by a summoning spell (see below). The duration of a calling spell is instantaneous, which means that the called creature can't be dispelled.
Subquestions
If a creature that used the ability enters the antimagic field, what happens?
The effect is on the creature? Or it was just the caster? The person with the active effect (it has duration left, even if undefined) will get surppressed.
Does a kitsune with the fox shape feat, in fox shape, revert to fox folk form or remains restrained to the fox form inside the antimagic field?
Yes, because her fox shape is a polymorph effect with a duration.
Does a sprite with supernatural invisibility becomes visible or does she remain invisible and cannot become visible inside the antimagic field?
Yes, she will become visible and won't be able to turn invisible again. The same will happen to an invisible stalker, they will show up as a ghostly vaguely-humanoid creature with no details (the picture we see in the bestiary), but they are no longer invisible.
Does a titan with change shape in human form revert to titan?
Yes, because change shape is a magical effect that has a duration.
Best Answer
It depends on how you define "area of effect," but probably not.
Invisibility states:
Pyrotechnics states:
So there are two interpretations:
Pyrotechnics is cast on the fire, which then has a harmful side effect (creating fireworks). This would not break invisibility.
Pyrotechnics is an area of effect spell, but simply doesn't note it in the summary due to the modality of the spell. This would break invisibility.
The key here is how you interpret this line:
Does the effect of "Fireworks" count as an effect of Pyrotechnics? Or is the effect of Pyrotechnics to generate a "fireworks" object that then generates this effect? The former will break invisibility, the latter will not.
As Pyrotechnics does not specify an area in its summary, I would lean towards Fireworks being created by Pyrotechnics, and invisibility not breaking.