The source code gives us the phrase fragment, which is understandable on its own....
The Fragments of winter which yield Words from word... are snowflakes!
Splitting the word "snowflake" in two gives snow and flake.

Click the snowflake and enter snow:flake as the authentication.

The first part of the source code i like to listen to it,
And the title Melody of winter... hint at an audio file.
The file winter.mp3 exists.

The second part of the source code and see what's inside of it,
along with the filename "spectrum" hint as using a spectrogram.
winter.mp3's spectrogram reveals 66+7+95+53+6/2+3+27+78+68.

To decode the numbers, use the area title Elementary table....
The elements abbreviations represented by the numbers are:
DY N AM I C and HE LI CO PT ER.

Click the level number and enter dynamic:helicopter as the authentication.

The title Memory of winter... and the comment a lossless winter hint at png.
This is because png is a lossless format of an image.
Find and open winter.png.

The image contains a set of black and white letters.
The catch is that not all colors are perfectly black or white.
Reading the "black" letters from darkest to lightest gives eldlich.
Reading the "white" letters from lightest to darkest gives cyberdark.

Click the level number and enter eldlich:cyberdark as the authentication.

The title Story of winter... hints at the file winter.txt
winter.txt mentions Lossy memory of moon which hints at moon.jpg.
The metadata of moon.jpg gives the artist dj TAKA feat. Erika Mochizuki,
and the title MOON. This is a real song.

The next part of winter.txt contains the lyrics of MOON.
Some of the words are replaced with a number.
Indexing the word with the number gives greatsorrow.
Navigate to greatsorrow.htm. The source code gives a set of instructions.

The instructions come in the form of "Move Column / Row X, In direction Y, Z steps.".
The origin of the grid is at the top-left column. It is also zero-indexed.
Tanpose the grid, and then use the coordinates provided in the source code of story.htm.
This will give you the words abyss and splash

Click the level number and enter abyss:splash as the authentication.

The title The last three letters... refers to xyz. The html name number is also important.
If you look up abyss splash, xyz, and number you'll find that this is a Yu-Gi-Oh card.
The card is called Number 73: Abyss Splash.
We can extract the number 73 as it is the only missing information from the level.

The source code gives (abyss, splash).
This turns into the coordinate (7, 3).
The image name is spiral.jpg, and we are told Going down, and up....
Using the altered grid from the previous step, and reading the letters in a spiral,
starting from (5, 5) and going to the right, and then down, until we reach (7, 3) gives
ghost belle x haunted mansion.

Click the level number and enter ghostbelle:hauntedmansion as the authentication.

The source code contains a set of letters separated by spaces.
Using the altered grid once again, find the sequences of letters in the grid.
Connecting them with a line in order will draw out letters.
This will form two words.

Click the level number and enter cruel:limits as the authentication.

The source code contains a set of six letters separated by spaces.
Using the altered grid, find the sequences of letters in the grid.
You'll find that the letters are all adjacent to each other.
For each group, continue the pattern and take the next letter in each line.
This will form two words.

Click the level number and enter pain:resonance as the authentication.

The title says We can't go back for now.... This tells us to stop using the previous grid.
The source code gives aleph-0, in eight.
This tells us to connect all אs to all 0s in all eight directions.
Doing so will cross out most letters, leaving only a few unmarked.
Reading the remaining letters in order of left to right, top to bottom gives op1feartitan.

Op.I《fear-TITΛN-》is a song written by xi and Kaneko Chiharu.
The area title tells us that In the last step, one doesn't coincide with roman numerals....
This refers to Kaneko Chiharu as xi is a roman numeral.

Click the level number and enter kaneko:chiharu as the authentication.

The title says Memory of snow.... This leads us to snow.jpg.
The reason we use jpg and not png is because of the source comment comes from story of winter.
Going back to the "story of winter" from Level 4 Part 1, we'll see that jpg is refered to.

snow.jpg contains red, green, and blue snowflakes.
To exact letters, overlay snow.jpg on the altered grid from Level 4 Part 1.
You'll have to stretch snow.jpg to make it fit nicely.
Reading the snowflakes in the order RGB yields the nurse dbd.
The name of the nurse from Dead by Daylight is Sally Smithson.

Click the level number and enter sally:smithson as the authentication.

The title says A tiny winter story..., therefore find atinywinter.txt.
The file contains a lot of text. Reading the first letter of each line gives NAMONAIHANA.

The soure code tells us You can translate, if you can....
Translating NAMONAIHANA from Japanese gives nameless flower.

Click the level number and enter nameless:flower as the authentication.