Getting White Day (2001) to run on modern systems without issues.

I'll expand later on this.

#1: Installing

Install the game normally
Just proceed, if your system is not Korean based (and assuming you are using the original untouched white day), proceed and in two text areas you should enter your name and organization or whatever.
Launch the game normally, if you encounter issues like graphics, black screens, random lighting and display objects proceed to section #2.

Set your PC locale or language for non-unicode programs (windows 10) to Korean, restart and the game should work. Continue in section #3.
If the first step didn't work for you or you don't wanna change locale, there is a further complex solution which requires installing a locale emulator, get locale emulator and install it.
Setup Locale Emulator to use Korean Locale or show it in context menu.
Right click on White Day shortcut or exe and run as Korean locale.
Click the first big text in the launcher, it will show a dialogue box about pentium 4 optimized code, click yes. (This was removed from the fan translated version which is why we're installing the patch manually later)

Game should work fine now, if you want to get English translation go to the next step.

Get the manual patch pack or whatever latest community patch version there is.
Copy all the files (if you just want the in-game translation then just copy over the .nop files) and things should be in English in game, aside from the launcher if you didn't paste over it's files.

In the games launcher make sure to choose DX8, 32 bit resolution and run the game with Locale Emulator or set your PC to Korean locale as in Section #2 always to avoid any crashes or bugs.

Oh! Jaemi is white day's official multiplayer mod that was shutdown sometime around 2005 or 2006, once enabled it could still be played in LAN, you simply need proper registry key for the option to show up in your launcher.
The game, even in LAN play mode, requires DirectPlay, an API which has been deprecated by Microsoft and is no longer part of DirectX future updates, however one can simply install it from Windows Features. (Hint: START + X -> Programs and features -> Install features).

Installing the patch manually without replacing the exe allows you to run the game normally with optimized pentium 4 code which means no bug would occur in game.
Our community will work on a better patch cooperating with all active members, moderators and admins here to provide a better translation and experience, we'll also translate the launcher and add few tweaks without messing with the code and causing game breaking bugs.
If you encounter further issues, trying setting compatibility mode on Windows XP mode, though normally this is not required.