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.
When I played and ran MERP, I alway took the world of Middle Earth to be a setting where magic is diminishing.
The mighty feats of the past ages are no longer possible in the current age. So, when you look at TA 3019 (the year of the War of the Ring) magic is mostly gone. However, we know that magic was much more prevalent beforehand. In the first it was ever present. In the second age, it was less powerful but nonetheless mighty feats were possible. Meanwhile, in the third age, less and less of it is visible or possible.
MERP is set in TA 1636 just after the great plague. This is 1383 years before the War of the Ring! So, there might still be a fairly large amount of "magic" about. Moria is still open and trades with everyone, Lorien accepts (reluctantly?) visitors, and Elrond's house is not a mythical place but just down this road. The Northern kingdoms still stand, although not for long. This is the time that Rolemaster/MERP try to model. A time where magic is rare but not uncommon.
The way I ran it is that Sauron, well, mostly his minions are actively hunting magicians to weaken the opposition. So, large displays of magic will attract unwanted attention. This forces the players to be careful and not lob fireballs at every encounter.
As for magic items, look at the Company of the Ring: they all have a dozen of them around! Most are very powerful indeed: Anduril? The Ring? A mail shirt of mithril?. Who can say that a +10 sword in TA 1636 does not become just a normal sword in TA3019 -- that is if it even survives that long!
Finally, what the system marks as magic and spells could just be skills by another name. Most of the channelling spells are weird channels of nature. Most of the mental spells are just that, your mind creating things. Essence is a little more difficult to rationalise this way.
TL;DR Basically the setting of Middle Earth of TA 1636 is what we see as high magical compared to TA 3019, but low magic as compared to the First Age. Rolemaster makes an okay system to model that: magic users are rare, for the most part, their spells can be rationalised as special skills, and them being blatant about magic will get you killed.
Note that this is to answer the question whether Rolemaster/MERP can be reconciled with Middle Earth. Clearly, I think it can using the above arguments. Whether it is a good model for Middle Earth is another matter -- I think it does a poor job. But that is a matter for either another question or discussion.
Best Answer
The Forgotten Realms is not "high magic"; it represents D&D's standard level of magic (DMG p.9, p23).
While magic is somewhat commonplace in the Forgotten Realms, this is really the baseline level of magic in Dungeons & Dragons 5th edition. The Forgotten Realms is defined in the rulebooks as a standard D&D campaign setting.
This is not to say that you can't run a campaign in the Forgotten Realms which is high-magic; the DMG explicitly tells DMs they may freely change the parameters of prewritten campaign settings. But by default, and canonically, 5e-era Faerûn is a world of standard magic.
What is the definition of a "high magic" campaign?
The term "high magic campaign" is not strictly defined in the D&D 5e core rulebooks, except to state that magic items are more readily available to player characters than standard (Dungeon Master's Guide p.38, Xanathar's Guide to Everything p.126). In a low magic campaign, by the same token, they are rarer than standard.
The standard campaign is the default D&D experience as described by the core rules. Dungeon Master's Guide p.9, "The Big Picture", defines the Forgotten Realms as one such campaign setting:
D&D's standard level of magic in particular is defined in Dungeon Master's Guide, p. 23, "Magic in Your World", making particular reference to the Forgotten Realms:
Eberron is then cited as an example of a world where magic items are more common than standard:
A formal definition of a "high magic" campaign can be found in the D&D 3.0 Dungeon Master's Guide (2000), p.164:
By this definition, Eberron is probably high magic in terms of magic items, though author Keith Baker avoids this terminology, as he considers the ready availability of high-level magic, which Eberron lacks, to be a defining trait of high magic setting. We see here that there is some subjectivity in the term's definition.
The terms "high magic" and "low magic" were infrequently used in WotC D&D products after this point, and even the 3.5 DMG omits these definitions. In the preview article Warforged, Shifters, Changelings, and Kalashtar in Your D&D Game (2005), Stephen Schubert states that magically created humanoid life forms may be commonplace in a high-magic setting:
In the Cityscape interview (2006), Ari Marmell describes high magic as something notably beyond the normal paradigm, though potentially local to a single place in an otherwise standard world:
Does the Forgotten Realms meet this definition of "high magic"?
No, not in general.
To begin with, the 5e Dungeon Master's Guide defines the Forgotten Realms as a standard D&D world, as mentioned above.
The Forgotten Realms Sword Coast Adventurer's Guide does not describe spellcasting classes as any more common than in baseline D&D. There are "a few" sorcerers in larger cities, and the are only slightly more common in some cultures (SCAG p.136); this concurs with the Player's Handbook which notes that sorcerers are rare. Wizards who advance in level find themselves with few peers.
Magic items are not described as any more common, cheaper, or readily available than standard D&D.
For more historic detail, the magic level of the Realms was canonically described in the D&D 3.0 Forgotten Realms Campaign Setting, p. 92, "Magic in Society":
The text goes on to describe that in the most concentrated places of magic, such as among high elves, the rate of arcane spellcasters is up to ten times higher, but that's still around 10% of the population, which is far below D&D 3.0's formal definition.
Even the World of Greyhawk, which sets the D&D 3e baseline for what is standard magic, has several high-level and epic spellcasters (the Circle of Eight, Mordenkainen, Gwydiesin of the Cranes) and several high-magic elements (the vanishing city of Rauxes, a shop in the Free City that straight-up sells any magic item, a nation-state run by a literal demigod, the Tomb of Horrors, Overking Ivid V's pit fiend ally freely casting wish, and numerous powerful artifacts).
The rarity of magic items, another defining factor in high-magic, is addressed on page 94 of the 3e Forgotten Realms Campaign Setting:
In a high-magic world, magic items are as commonplace as modern technology, so most people would have a magic cooking pot. In 3e-era Faerûn, they are rare enough that only the richest might own one.
Further, magic items are described in this book as primarily obtained by looting ancient sources, as well as produced at great expense by temples or the Red Wizards. This isn't the "bought and sold in clearly marked shops like any other commodity" of D&D's "high magic"; magic items are found or commissioned specially, and adventuring magic items are rare.
Magic of Faerûn p.136 says that hundreds of magic items are made each year; not quite the thousands or millions one might expect if it were as commonplace as modern day technology. Page 64 of that book notes that the open market is largely full of superstitious charms instead of real magic items, with the few real sellers operating secretively or on the black market:
Magic items aren't widely sold openly, in clearly marked shops; according to Magic of Faerûn p.65, Risa's Shop in Baldur's Gate is specifically unmarked, operates secretively, and is available by invite only. Shalush Myrkeer secretly operates a secret auction once per year in a warehouse upon the full moon.
Races of Faerûn does describe certain magic items as "common items" among certain races, but the definition of that term on page 5 is merely an item regionally available at a 10% discount due to it being more prevalent than usual. The average shield dwarf still can't afford to buy a +1 keen battleaxe; it costs 7,479 gp instead of 8,310 gp, but that's still beyond most NPC fighters' budgets, so it would be a misnomer to say these items are really common, and inaccurate to infer that magic items are generally common in the Forgotten Realms. It's not the same definition of "common item" used in 5e's Xanathar's Guide, which instead represents very minor effects like automatically-mending clothing or an orb that tells which way is north.
What's more, this was all 3e era—the canonical 4e and 5e Forgotten Realms transitional cataclysms are likely to have reduced the setting's magic even further since then. Notably, the Spellplague weakened some items and violently reduced the number of spellcasters:
Summary
The Forgotten Realms is a magical world with some exceptional elements, but it is not high-magic by the standards of Dungeons & Dragons. In D&D 5e this is even more true, since Forgotten Realms now increasingly defines the standard level of magic for Dungeons & Dragons, and historic changes have significantly reduced the amount of high-level magic in the world.