You make me blush, lol.
As I said I'm really, reallly noob at hacking (This is my first effort besides sprite editing and some text changes), so the bit sequences knowledge is totally something I lack. It's used in several places, like in Steal mechanics too.
I'll try to answer your questions:
About the elements and status values, most of them are used by the game itself, if you go to the enemy portion of the code (Starting at 60010) or weapon/armor data you can see them. I find them pretty high too, but if that's what the developers used there must be for a reason. Probably most of what I listed are repetitions of what could be an original value, but if it's that way, why they wouldn't use it?
It's like the repeated Recovery Element. There are many values that add Recovery, yet the game only uses 01. I think they just added things "just in case" and never used them (Like the equip bonus list, my god that was long).
Something that I found looking at the game is that there's a lot of things that went underused, and if the game is already one of the best on the Famicom, imagine if someone with real skills went to tinker with it.
The status effects don't play a big part of the game, except for some enemies to make them annoying. I added status to weapons to make them a little more interesting.
Petrification and Partial Petrification 2/3 are broken as hell, I had to remove them from weapons because they activate almost everytime.
the Targeting system was a pain in the butt to get listed. Why would put so much space into repeating so many values? There doesn't seem to be any difference in them, more than having several values for each magic level... And it only changes what they can target in battle, so I really don't see that much reason to have so many.
And yes, my mind was full of s**t when I saw that the very value list for weapons and armor is used for spells. Just...Wow. It's both weird as hell and somewhat convinient as well.
But anyway, yes! If you can give MP to a class (Both by figuring out how the level up gains are, which because they must use bit sequences i'm totally lost, or by giving them a set of MP to a class in the "Base Stats section") and put a spell within it's own Class Usability group, and lastly give him/her the Magic Command...
Well:

I gave him the value 1F in his base stats:
5B 0E 14 0A 0A 05 0A 00->1F To give him MP from that table (That's not used in the game, by the way).
Then i changed the Class Usability Group from the Safe Spell to 87 (Only Dragoon for Armors, to make an example)
And then changed his Defend Command (05) to magic (15) and Voila, Casting Dragoons!
I really liked the idea of giving classes their own special spells, but it's far from my abilities and maybe I'll consider doing it in the future, as my actual romhack was about trying to improve here and there things without making giantic changes (Improving a little the original, more or less).
I just checked, and I need to correct that part: If you put 30 to one spell, the only change is that the spell becomes Single Enemy/Ally Target. The spell will do whatever it's supposed to do in battle, and outside of battle won't do anything if the spell didn't do anything before.
That's a total fail for my part, sorry.
By the way, what a spell does in and out of battle doesn't seem to be the same. For one, you don't heal the same ammount of HP outside of battle as you do while fighting, and there are several white spells that you can multi-target while in battle you can't (Mini, Toad, Pure...). Warp lets you teleport to other floors of a dungeon, but in battle is a Kill type spell).
Now, I said that "it won't do anything" originally. That was because of the value 0C.
61A80 Sight 00 64 00 00 0C 30 00 32
If you give any spell 0C it won't do anything after it's animation.
The Unknown spells... Yeah, I call them unknown because I can't really see what are they. I'll add their code so you can see them.
They have a power level that doesn't seem to exist in any list of magic anywhere, the Usabilty Group is one that is never used, But if you look at the list, it could go there (It stops at 3E), they use totally different values for targeting, and if you try to copy the code over a known spell, what you get is that the spell is automatically targeted to the caster and will damage him/herself.
About the missing commands, 01, 02 and 03... Well, they are this:

Anything that it's not listed will bring glitches and garbled bits of battle text. Kind of a letdwon, I was expecting secret commands... But they only crash the game.
What I wasn't expecting is so many equipment boosts. Jesus Christ they went out of their way with that. Alongisde Steal and drop mechanics, this is the other thing that screams "WHY DIDN'T YOU USE ME".
By the end of writing all of the effects my eyes couldn't see s**t because of how tired they were.
About the "First Weapon"...
I think you're right. At first I thought it would be 616C8.
But that can't be it, because 616C8 (Which is 00 00 00 00 00 00 00 80) has an Armor value, while 61410 has a Weapon Value (00), meaning that it can be "equipped by" anyone. Another oversight on my notes, i'm sorry.
The order of the weapons is mostly consistent, there are a few entries out of order (Axes and hammers where swords are, dark swords and normal swords mixed too...)...
The Hammer is a dummied weapon, you can actually bring it back to the game (Just like the Dream Harp, which I did in my hack) by putting it in a chest or store.
About the Axe in IV... I think Squaresoft hates barbarian weapons :( .
There seems to be none of the racial bonuses in this game, more than, maybe, the "hand made" Dividng monster's "weak to dark swords". But that's just a combination of a Weapon Usability Group Value and the Dark Element on a weapon. Kind of weird, seein how games before and after it have that sort of feature.
FF3 seems to have quite a bit of variety in it's weapons design, which is kind of surprising. The funny part is that you can make weird combinations if you want. The most cool ones are the Boomerang/ Moonring animations with anything else.
57 is Empty Space, yes. If you put it in a shop, you can buy it! It cost 0! What a rip-off.
The item list was used pretty much at it's full potential, which is good for one part (They made lots of items) but if you want to create something you'll need to expand or remove something before...
All the things we talked here have been corrected on the text file, in case you want to get it again.
I really don't know what more I could say. I could explain monsters a little, although the only thing i've modified about them is HP, Int/Skill and weaknesses, but i wrote pretty much all i learned doing this.
Maybe a Monster List can be helpful, some of them are in weird spots (Unei Clone is almost at the beginning of the list!).
About my hack, I finished playtesting it, and finished fixing things before I went to sleep. I must now finish the aesthetic patches (Menu/Character palettes, optional stuff) and then I think i'll try to upload it to RHDN, if they see it worth enough of being there, of course.
After that I'll take some "vacations", because this has been taking too much free time out of me.