Primefusion

To be a little more specific:
- Open up NUPS and select "Create a new UPS patch" button.
- Select a clean ROM, your edited ROM, and where/what to call the patch.
- Click the Create Patch button
- Profit

Agro phrased things wonky, which I think is causing some confusion.
There's two key arrays going on*: the chapter array, and the event array (what people tend to call it). The chapter array is what you'd expect: it's got entries for Battle Before Dawn, Cog of Destiny, etc. Each chapter has several indexes to entries in the event array. Except the event array has much more than just events. It's really an array of pointers to things like tileset data, tileset palettes, tile changes, and yes, events.
It's more like a "Things a Chapter Needs" array.
Each index in the Chapter Needs array can be a pointer to whatever you want really. Know you're not going to use the lava tileset? Make those pointers point to events instead. In the chapter data editor, you can take one of those cut-scene only chapters, and point to the new event pointer you made.
*There's more than two arrays getting used, but these are the big two. Death quotes and support conversations each have their own array.

Try the instructions here.

Try tearing out the Mode 2 and Mode 4 sections. FEditor creates those automatically when reading scripts.

It lives here.

OAM data overflow usually means that your animation has too many frames, or that too much changes between frames. As far as I know, there's no way around this other than adjusting your animation accordingly.

I've got a hunch the issue might be that you're using the .bmp versions of the tilesets, which I remember not being reliable.
Trying making a quick map from the tilesets found in this topic (They come with the Mappy download), and report back.

There's a bunch of hard coded shenanigans surrounding hand axes that makes adding more of them challenging.
If you want to add more, you have to setup a custom animation pointer for each axe wielding class and add the new hand axe to the list (this gets tedious fast, especially if you want to add additional weapons later).
Other than that, or some solid assembly programming, you're limited to the 3 vanilla hand axes.

I just use a bunch of character slots for the different classes and make palettes for each of them. It's a lot of work, but the palettes turn out exactly how I want them too.
I had that problem too, but then stumbled upon this snippet. Give it a whirl:
UNCM SybarisMerc 1b // SybarisMerc is the one that dies FIGH AksumCavalier SybarisMerc MapFight1 $0000001F // force them to use an iron axe. Since mercs don't have an axe animation, it becomes a map battle. UNCR AksumCavalier 0x02 // Revert the cav from being grayed out after battle.

As of yesterday there's one in the animation topic (along with some other animations for the ladies).

There's two parts: The text and the events.
In the text slot where you're showing the "Will you do a thing?" text, you'll want to put a [Yes] tag, which will show the yes/no options.
Second, in the event, you'll want to set up a IFYN condition immediately after the text. Example:
Text(0xYourTextIdHere) // Has the yes/no text IFYN 0x01 // If yes was chosen ELSE 0x02 ENIF 0x01 ELSE 0x02 // If no was chosen ENIF 0x02

Use the Custom Battle Animation module. Once you've got the animation settings in place, assign the pointer the module gives you to Roy's class.

What you're referring to as "turning on/off enemy growths" is toggling whether or not they're auto-leveled.
I've got a strong hunch that the game rolls level ups for each enemy that has auto-level enabled.
Current level - base level = the number of level ups rolled per enemy. Each chapter also has a hard mode bonus you can change via the Chapter Data Editor. This gives all enemies an additional X level ups.
The reason you're seeing the variation is that enemies, like player units, don't always get the same stat procs per level (The RNG giveth and taketh away).
Hunting down any formulas would require using a debugger to do some tracing. I would ask around on FEU to see if anyone has notes.

I prefer FE Recolor to make the palette, then using Kagnus's Inserter to stick it into the ROM.

Two steps:
1) Enable it with the chapter data editor.
2) Have your opening event end with ENDB instead of ENDA.

Enemies use class growths for autoleveling. An enemy's stats will only increase beyond their bases if autolevel is set to true for the unit in question.

You can make tile changes occur manually by using MAC1, MAC2, or MAC3 (Check Event Assembler Language.txt for the syntax).
If you're unsure which MAC# command to use, check this topic.

You wouldn't have a "byte point at an assembly routine". You would edit the battle calculations routine(s) and check if the combatants have the skill(s) you're looking for and act accordingly.
Or in the case of the Pick skill, you'd edit the routine that checks for lockpicks and keys to also check for the Pick skill so that the menu would display the Door/Chest command.

In FEditor's Doc folder there's should be a Text Control Codes.txt file, which specifies how to use them. If you're not already, I also recommend referencing the original game scripts which you can dump using FEditor's Text Editor.
To have a portrait jump, just have it move to the spot where it's already standing. Example: If it's at MidRight, use [MoveMidRight].

To fix the experience gain issue, you need to edit the "This class promotes to X" value in the Class Editor for each offending class. Set their promotion class to a valid tier 1 unit and they should gain and give the correct amount of experience.
Not too sure on the effectiveness issue. What do the class lists you're pointing to look like?

You'll need to use 2 chapters slots. When it's time for the goal to change, use LOMA in your events and load the chapter with the updated goals.
A word of caution: Once you LOMA and the current scene ends, the game will begin to use the events of the newly loaded chapter. So, if you want all your events in one file/spot, make sure both chapter slots use the same set of events.

There's a couple things that might have gone wrong.
1) You had Nightmare/FEditor open both before and after you reinserted the map, and then when Nightmare/FEditor was saved it undid everything.
or
2) The pointer to the new map wasn't set up correctly.
Try inserting the map again, but make sure neither FEditor nor Nightmare are open. Then, go in afterwards and make sure your pointer is set up correctly.

Since you're using a 16 color palette: did you repeat your palette 4 times?
I probably could have been more clear about this, but you'll want to copy/paste-overwrite your palette so that it's repeated 4 times.

If your chapter uses a prep screen they should be loaded automatically. If it doesn't use a prep screen I'm not too sure. Try looking at some of the disassembled vanilla events to see how they did it (If at all).

Sounds like you have an incomplete/out of date package then. Make sure you grab the latest from the Resource Directory.
They'll be in the Battle Palette Editors folder.