This will be based mainly on Pathfinder, as this is the system I play in. Adjust for your own rules. Note that for a lot of your questions, there is no very specific RAW answer (this is often the case with Antimagic Fields). I indicated all the RAW points and the most probable/logical result, but in the end there is still a lot of room for DM interpretation.
First, let's mention that technically, DMZ are AMF for all purposes. There is one big exception that I will mention below, though. Now, on to your questions.
Do potions work at all? In an DMZ, there is no conduit for magical Energy. It's clear to me that a potion is used up, but what about the (clearly magical) effect?
This is a tricky one. You can find a discussion about it here. Remember that potions are "a magic liquid" that "duplicates the effect of a spell". There seems to be 4 possible situations, based on the effect duration (instant, not instant) and where you drank it (outside or inside the zone).
- Drunk outside: no issue for an instant effect, as the effect has been applied already.
- Non-instant effect, drunk outside: the effect is suppressed, but not dispelled. Time spent inside the zone count against the duration.
- Non-instant effect, drunk inside: logic would seem to dictate that as for a spell, the effect is suppressed, but not dispelled, and time spent in the zone counts against the duration. So a character using a fly potion would not start flying, unless he got outside the zone before the duration expires.
- Instant effect, drunk inside: if we follow the same logic as the previous point, the potion wouldn't work when drunk, and since the duration ends immediately, would have no effect when outside the zone either.
It is clear to me that if the weave is not existent, wands/dorjes won't work. Do they still lose charges?
Grab a pencil next to you, and yell "Fireball!". Chances are, nothing happened (if it did, I am really sorry).
Normal items don't recognize triggers, this is a function of magic items only. Since a wand in an AMF is just a piece of wood, it has no ability to recognize the triggers. The magic triggers and even the magic charges don't exist while in the field.
Again, this is subject to DM interpretation, as you can cast spells inside AMF.
In an AMF, incorporeal undead cannot exist (winking out). Does that work the same way in DMZ?
That's very interesting and I never realized it before. I mainly use the SRDs (d20pfsrd and Paizo's), which both say:
Summoned creatures of any type wink out if they enter an antimagic
field.
No mention about Incorporeal. Searching around, I finally went to get my Pathfinder Core book, which reads:
Summoned creatures of any type and incorporeal undead wink out if they
enter an antimagic field.
As you said in a comment below, this seems to result from an errata, and the correct version does not include Incorporeal undead winking out.
However. Incorporeal undead live in the Ethereal Plane. Affecting the Material Plane is done through (Su) abilities, and seem to be definitely magic by nature. So we can assume than in a DMZ as in an AMF, Incorporeal Undead are stuck in the Ethereal Plane with no way to affect the Material Plane.
What about corporeal undead, animated by magic? These "work" (read: continue to be animated) inside AMF; what about DMZ?
As you said, it works in an AMF, and a DMZ works similarly to an AMF, with a non-negligeable exception that I will mention soon. However, instead of just saying "Undeads work in an AMF, DMZ are AMF, undeads work in DMZ", let's check the logic behind.
Animating dead is an instant effect, not a long duration one. Therefore, once animated, the Undead are not magical. They cannot be dispelled, the same way that you can't dispel a Cure Light Wounds spell after it has been applied. So since their being animated is not a magical effect, it does not need the presence of magic.
The other reason is a balance one. AMF is not intended to destroy creatures. It can hinder them, but not kill them. That's why it has no effect on golems or outsiders either.
Finally, note that controlling undead is in some cases a sustained magical effect. So while being animated is not affected by an AMF or a DMZ, being controlled can be. This can lead to... interesting situations.
The one difference between Antimagic Fields and Dead Magic Zones: Shadow-weaving
In the Faerun setting, Dead Magic Zones represent a dead part of the Weave, the fundamental part of magic (arcane and divine).
However, the Shadow Weave is distinct (and even opposite it seems) from the Weave, and thus is not affected by DMZ. This means a Shadow Weaver can cast spells in a DMZ without any issue. You could argue he would be restricted to Enchantment, Illusion and Necromancy though, as they are the most 'Shadow Weavey' schools.
Note that this also mean that magic items crafted by a Shadow Weaver could theoretically work in a DMZ. This would affect the potions and wands points above. No effect on incorporeal/corporeal undead points, except a Shadow Weaver would be able to control Undeads in a DMZ.
Houserule out the "Control" aspect from the spell.
The problem with the spell isn't so much that it calls in powerful monsters, in my experience. It's that it instantly gives you powerful but obedient slaves.
Calling in a Solar or similarly powerful creature isn't something I would like to cut from my D&D experience. What I would like to cut out is that any random Wizard with 9th-level spells can call in a Solar, tell it to make a sandwich, and it goes "yes master". There's no defense against this mind-control for the Solar, no saving throw, no action requirement, just control by the caster as soon as the creature is through the Gate. And that allows shenanigans, increasing the caster's ability scores being the least of which.
Now, if that control were removed, it would remain a powerful and supremely useful spell. You can still call in a Solar when your party is fighting a Balor, I'm sure the celestial would be thrilled to join the fight. You could call on it for advice. You could even ask it to increase your ability scores, which it might, could you convince it your being slightly more intelligent/strong/quick/whatever is a worthy use of its Wish ability. You just can't make it do things it ordinarily wouldn't do, by virtue of the Gate alone.
As a bonus, I'd say the spell now has far more narrative potential. "YOU DARE SUMMON ME, MORTAL?"
Best Answer
This list is not exhaustive, just off the top of my head. Note that these defenses protect against a lot of dangers, not just dispelling, and certainly not just the dispelling of permanency’d effects, which would generally be on the low end of people’s priorities. Persistent, rather than permanent, effects would generally be more important.
Bonuses to caster level
Caster level is valuable to spellcasters. Gaining bonuses to it is well worth one’s time. A prayer bead of karma is remarkably affordable for the effect (and can even be used on arcane spells if you have at least one divine spell or a decent Use Magic Device check). An orange ioun stone is much more expensive, but still well worth it.
Bonuses to the DC to dispel your stuff
Less common, but when available often in larger amounts. Master specialist is a commonly-used, easy-to-enter wizard prestige class that offers some, for example.
Protections against dispel magic and greater dispel magic
These spells are very dangerous to anyone in 3.5, so protections against them were commonly sought after. Having a ring of counterspells keyed to dispel magic and later greater dispel magic was a common tactic. A ring of spell-battle is also often useful.
Simply getting the drop on opponents
And this was the big one. If you really were going in for high-optimization tactics, that means you weren’t giving opponents a chance to cast anything. Scry ‘n’ die, heavy initiative optimization (and at high levels, greater celerity and shapechange into a dire tortoise just to make sure), potent defenses even to the point of literal invulnerability, and so on. The black tactica build specialized in counter-nuking and definitely would not allow a greater dispel magic to be cast by anyone near it.
Contingency
And then the final nail in the coffin, somewhere buried under all that there is likely a contingency spell. Which could very easily be used to, say, greater teleport to somewhere safe as soon as a greater dispel magic spell was actually successfully cast on you.