They are all packed in the file "resources.assets" which is present in the folder
C:\[Steam Folder]\steamapps\common\FINAL FANTASY IX\x64\FF9_Data
Depending on you installation, it may be the one inside x86\FF9_Data instead that is used.

You need an Unity Assets archive browser to access to them (.assets are like .zip, but fewer programs can extract files from them). UnityEx is good for that.

Texts are split between several files in this archive. Namely, you've got to extract those :
Battle Texts "[nb].mes"
Field Dialogs "[nb].mes"
World Texts "[nb].mes"
Field Names "loc_name.mes"
World Places "worldloc.mes"
Spells "aa_name.mes" "aa_help.mes"
Supports "sa_name.mes" "sa_help.mes"
Commands "com_name.mes" "com_help.mes"
Items "itm_name.mes" "itm_help.mes" "itm_btl.mes"
Key Items "imp_name.mes" "imp_skin.mes" "imp_help.mes"
Battle Infos "follow.mes"
Battle Scan "libra.mes"
Battle Spell Naming "cmdtitle.mes"
Choco Menu "ff9choco.mes"
Card Titles "card.mes"
Card Names "minista.mes"
Tetra Master "minigame.mes"
Other Menus "Localization.txt"

Besides "Localization.txt", there are always 7 of them, one for each language. The last has a format a bit different ; all the languages are in the same file.

Texts end with the code [ENDN].

Thank you for such a detailed answer. I go see what's there.

By the way, I just saw that the formatting in "Localization.txt" is buggy.
Language texts are comma-separated, just like this :

Item,Item,Item,アイテム,Objetos,Objets,Item,Oggetti
Use,Use,Use,つかう,Usar,Utiliser,Benutzen,Usa
Arrange,Arrange,Arrange,せいとん,Ordenar,Ranger,Ordnen,Ordina
KeyItem,Key,Key,だいじなもの,Importantes,Trésors,Wertvolles,Rarità

However, there are several texts with commas inside, which shouldn't be separators but are still handled like ones by the game... They cared about the english texts (there are few commas in them and when there are some, they are wrapped inside quotes so the game read them properly) but the other european languages have bugs because of that.

two clarifying questions:
1) by which program is best to edit text
2) how to save changes to a file "resources.assets"

UnityEx can re-import the text file inside "resources.assets".
As for texts themselves, you can edit them with any text editor (notepad++ for instance).