Before I post this I would like to point out that I in no way found all this information out on my own. I simply compiled it, tested it, and tried to make sense out of all the misinformation on the password list. My thank to ForteGSOmega, xDark_Shinobi, all the people compiling and translating the game info on the various wiki's and the translation spreadsheet.
Now I may have gotten something wrong, this took awhile to gather together so I may have mixed up what an item is supposed to do or mistaken it for something else but I tried to make it as accurate as possible.
To use the passwords, go into Jijimon's house and access the computer behind him. It will be the first option you need to select, and afterwards you can type in your password. Now mind you, some passwords will not work at first, such as the Colosseum ones. You need to unlock either NPCs or specific floors of the Colosseum before they will, but I'm not entirely sure when each one activates seeing as how I typed in all 52 passwords after I beat the game, beat every battle and tournament in the Colosseum, etc. So I can't help with specifics. Also you have to check your email log ingame when you use a password, otherwise you won't notice anything new. Now then before I ramble on some more, here's the list: