I agree with both of you.

Naming dirs and files can help people understand where things are located and such, but as Cyberman pointed out it is too early to do that. I'd suggest to simply create tables mapping the numbers to a short description so people interested can use them and don't get lost. But I'll keep on using numbers until things are a little more clear. (Anyway I wouldn't mind explaining something without the numbers if necessary.)
I think the table Zande provided for the directories is a good start. Now that I can read some of the encoded text, I'm doing a similar table for files in DIR00 in my free time (not much).
For those interested in reading the encoded text I found, I'll post this table:
0 1 2 3 4 5 6 7 8 9 A B C D E F
+---------------------------------------------------
0| 0 1 2 3 4 5 6 7 8 9 + - = * % SPC
1| A B C D E F G H I J K L M N O P
2| Q R S T U V W X Y Z ( ! ? " : .
3| a b c d e f g h i j k l m n o p
4| q r s t u v w x y z ) , / º ~ &
5|
6| á Ã
7| ó ú
8|
9|
A|
B| ¿
C|
D|
E|
F| \n
SPC=SPACE (0x20)
\n=New line
It's not complete, as I've added only the bytes I verified, but it should be enough to read some text; especially the dialog, some debug messages, and the text from the menus.
The row number is the most significant nibble in a byte and the column number is the less significant nibble. You'll have to convert that byte to the character inside the cell in those coordinates.
It's not too difficult to get the position for other characters as they can be found in some of the TIM images of fonts.
I already know how to get the image for each individual character from the font image, but I haven't looked too much into it so I'll leave that for when I have more time.
If anyone feels like completing the table I won't mind.

A note: there are probably similar tables for other fonts.
Besides that, I have a description of what I know is inside of F<00>013. It's interesting as I was able to recognize most elements from the first half of the file, but I think I won't be able to know what's inside the other half just by looking at it.
File F<00>013 seems to be the "load/save game" menu. Just to give some bad news to Cyberman

, I wasn't able to find a header nicelly describing the components, plus I think it's the same thing for all DIR00 files. My only hope is that those elements are pointed to from a script.
I won't give the offsets of my version, as they'll surelly be different for the English version; or any other language for that matter.
(4 bytes) File identifier? (=0x00000014)
(4 bytes) Unknown (=0x00003030)
(8 bytes) String "/DISCO" padded with 0x00. (Translation: "DISK")
(4 bytes) Unknown (0x00)
(2 bytes) Unknown (0x7e)
(2 bytes) Unknown (0xe0)
(4 bytes) Number of pointers to strings that follow. (=0x3a)
Pointer to string:
(2 bytes) Number of bytes (relative to offset of first pointer) till the first char of the string.
(2 bytes) Unknown. (Attributes of string?)
... (Repeat for every pointer.)
Encoded string. (Variable length.)
... (Repeat for every string.)
(256 bytes) CLUT for Zidane. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Zidane's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Vivi. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Vivi's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Garnet. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Garnet's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for ***. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of ***'s face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Steiner. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Steiner's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Quina. (entires=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Quina's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Eiko. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Eiko's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Freya. (entries=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Freya's face. (width=32, heigth=46, size=1472 bytes)
(256 bytes) CLUT for Amarant. (entires=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Amarant's face. (width=32, height=46, size=1472 bytes)
(256 bytes) CLUT for Marcus. (entires=128, 16bpp, size=256 bytes)
(1472 bytes) Picture of Marcus' face. (entries=128, 16bpp, size=1472 bytes)
(512 bytes) CLUT for "passing pages of a book". (entries=256, 16bpp, size=512 bytes)
(5808 bytes) Picture of "passign pages of a book". (width=176, height=33, size=5808 bytes)
... (Rest is unknown at the moment and is barelly half the file.)
The *** above means I don't remember the name of the protagonist, but if I'm not wrong it's Dagger. I really don't remember if Garnet changed names and the picture of her face changed in the menus as well.
The "passing pages of a book" is, as I mentioned before, the animation of the book that appears when the game is opening a memory card.
After that image I don't know what's in there. That may be a good place to look for some script or compiled code but I don't know machine code nor assembly for the psx and neither do I know ff7 nor ff8 scripting language. So, if anyone could look a little bit into it, please...

It's quite homogeneous and if it was a 8086 architecture I'd go for code, but I might as well be completelly wrong.