Recently I've been hacking the European version of Final Fantasy 4 Advance, and have made notes on its data structures, ASM code and AI scripting as I went along. Since there doesn't seem to be much documentation on this version that I could find, I though I'd share my notes here.
This is a link to my notes, including modules for use with the Nightmare table editing program (not very flexible, but it's dead easy to use). It includes documentation on item,spell and monster data, encounter sets, encounter setting (eg. what music to play, whether some monsters start out hidden), monster AI, chest contents and more; the bulk of my notes are in "ff4a-structs.txt", which was originally based off of notes by PKT Paladin.
I've also written some custom ASM code for a little hack of mine that might be helpful to others.
More variance for encounter RNG
If you've played FF4a before, you probably know how the encounter system is messed up: the same battles tend to occur over and over again, and saving+loading doesn't help. This is mostly due to the fact that the RNG used to determine what you encounter and when is seeded from only one thing: the amount of time you spend on the file loading screen. This tends to produce very similar seeds, leading to the same pattern of encounters recurring.
This code fixes this problem by seeding this RNG with your save file's game clock in addition to the above:
$0827E6: 2188 401A 0F49 6052 3CF0 D3FA 2188 4018
Paste write the above byte sequence to $827E6 in the FF4 Advance (E) ROM.
Allow monsters to use their Magic Defence Multiplier
Normally, a monster's MDef Multiplier in the ROM is never written to their RAM battle data. To undo this, make the following change:
$93082: Write 0000
Note that all monsters have zero Magic Evasion by default, so you'd need to give them values yourself.
Back Row functions almost properly
In the European version, melee weapons have no penalty to Attack or Precision for attacking from the back row, while the actual long-range weapons (Bows, Harps, Boomerangs and Whips) do receive a penalty. To fix:
$8A858: 07D1
$8A868: 00D0
Currently my code fixes this by making your attack Back Row-Ok if you have any long-ranged weapons equipped, which means that Edge with a katana and boomerang can attack at full power from the back row. A more nuanced fix requires more space (and therefore repointing code).
Modular elemental weaknesses from armor
By default, armor that resists Ice or Fire is hardcoded to give a weakness to the opposing element, unless your equipment protects against Fire,Ice and Lightning all at once. This code ties elemental weaknesses to a byte in armor's affinity data instead:
Equipment (including weapons!) can have elemental weaknesses that apply to the actor (byte 0x1 in affinity data):
Start of Battle $9F440: 4178 0023 0B43 A08C 1FF0 A8FC 4178 0B43 A08D 1FF0 A3FC 4178 0B43 E08D 1FF0 9EFC 4178 0B43 208E 1FF0 99FC 4178 0B43 2222 AB54 28E0
During Battle $9DA2E: 4578 B88C 21F0 ADF9 4078 0543 B88D 21F0 A8F9 4078 0543 F88D 21F0 A3F9 4078 0543 388E 21F0 9EF9 4078 0543 2221 7554 29E0 0000
Monsters' basic attacks can be imbued with elements (byte 0x6 in monster elemental data):
(ASM) $7F7000: 5088 A083 9088 2084 9079 6076 3188 7046 0430 0047
(ASM) Link from $93156: 0148 2BF0 12FE 01707F08
Simple- this lets you have Fiery Hounds attack with a Fire element. Handle with care: elemental physical attacks do triple damage when hitting a weakness!
Reworked Boss Bit vs Status system
By default, enemies with the Boss Bit are protected against all forms of status (but Slow/Sap), and a few other things besides. This code moves it closer to the SNES system, where status spells only fail against a boss if the spell also has a boss bit.
New system: Boss bit only prevents status spells if they have a boss bit too!
Regular status resistances still apply, however.
Byte +$07 of spell data is the boss bit; if bit 00 is set, the spell will fail against enemies with the boss bit.
Status spell logic:
$8B02E: 5B49 084B 795A 0901 5B18 D879 0121 0140 0029 06D1 09E0
$8B054: 2890E008
Updating Bestiary screen:
$121D0: 00000000
That's all I've got for now, but I might have some other things to show at another time. 
The European Version is normally considered to be the superior version all around. I'm surprised to know there is still so much wrong with it! Well we are glad to have a compatriot working at other angles to fixing FFIV and maybe we can learn a couple of things from one another.
Allow monsters to use their Magic Defence Multiplier
Normally, a monster's MDef Multiplier in the ROM is never written to their RAM battle data. To undo this, make the following change:
$93082: Write 0000
Note that all monsters have zero Magic Evasion by default, so you'd need to give them values yourself.
Wait a moment... are you telling me that FF4A goes a Step further and outright removes Magical Defense Multipliers from enemies? Granted they are non functioning without Magic Evasion, but that... seems so bizarre. So does FF4A actually have the code to properly place Evasion and Magical Evasion in an enemy's stats or is That still busted from the SNES version?
Back Row functions almost properly
In the European version, melee weapons have no penalty to Attack or Precision for attacking from the back row, while the actual long-range weapons (Bows, Harps, Boomerangs and Whips) do receive a penalty. To fix:
$8A858: 07D1
$8A868: 00D0
Currently my code fixes this by making your attack Back Row-Ok if you have any long-ranged weapons equipped, which means that Edge with a katana and boomerang can attack at full power from the back row. A more nuanced fix requires more space (and therefore repointing code).
Ugh... I had thought this was supposed to be fixed in the European and Japanese version? I guess not... This is a fine fix and the Boomerang/Katana mix makes it the same as what every version of FFIV has allowed. So don't worry. Even Square thought it was too much trouble to bother with.
Modular elemental weaknesses from armor
By default, armor that resists Ice or Fire is hardcoded to give a weakness to the opposing element, unless your equipment protects against Fire,Ice and Lightning all at once. This code ties elemental weaknesses to a byte in armor's affinity data instead:
Equipment (including weapons!) can have elemental weaknesses that apply to the actor (byte 0x1 in affinity data):
Start of Battle $9F440: 4178 0023 0B43 A08C 1FF0 A8FC 4178 0B43 A08D 1FF0 A3FC 4178 0B43 E08D 1FF0 9EFC 4178 0B43 208E 1FF0 99FC 4178 0B43 2222 AB54 28E0
During Battle $9DA2E: 4578 B88C 21F0 ADF9 4078 0543 B88D 21F0 A8F9 4078 0543 F88D 21F0 A3F9 4078 0543 388E 21F0 9EF9 4078 0543 2221 7554 29E0 0000
This is a really neat idea for those who don't want Weakness tied to basic Element. I may have to consider something similar for FFIV down the line. I've taken a look at your notes and FF4A has a boatload of more room for what to do with Weapons and Armors! FFIV has to rely on a stringent Bonus Index which forces down possibility by a fair amount and has a more open accuracy system where as FFIV has a basic (00 = 00 Accuracy) (63 = 99 Accuracy.) with only 8 Bytes to each weapon instead of 12 and the same 8 bytes for Armor compared to !?20?!. What I think I could do is tie it into that weird unused "item type identifier byte" which to my knowledge doesn't actually do anything. You also managed to put it on Weapons though which would be a much tougher sell all around in normal FFIV.
There is also some interesting notes on spells you have here! Again they've really increased the possibility there. Even allowing easy access to previous Routine-set statuses.
Monsters' basic attacks can be imbued with elements (byte 0x6 in monster elemental data):
(ASM) $7F7000: 5088 A083 9088 2084 9079 6076 3188 7046 0430 0047
(ASM) Link from $93156: 0148 2BF0 12FE 01707F08
Simple- this lets you have Fiery Hounds attack with a Fire element. Handle with care: elemental physical attacks do triple damage when hitting a weakness!
They removed this functionality? Yes, it was unused in SNES FFIV, but it still functioned to my knowledge if you implemented it on monsters.
I am looking forward to hearing more from you! Your notes may be of use to us here and vice versa.