It's mainly about the daily lives and relationships of a group of teenage boys. The story focuses on their friendships, emotions, and experiences growing up.
The difference between passing a day like a year and passing a year like a day was the feeling of time and the state of mind. Time passed very slowly, probably because of the pain or hardship of life. The passing of the year like the sun meant that time passed very quickly, and the year flew like a day, perhaps because of happiness or anticipation. These two idioms describe people's different feelings and attitudes towards the passage of time.
The Kagerou Days Manga Story has a complex plot involving time loops, different characters' fates, and a mysterious world. It mainly follows the story of a group of teenagers with special abilities. There are conflicts, friendships, and lots of emotional drama.
I'm not sure specifically as I haven't read it. It could be about various things like the adventures of the characters during 340 days, or it might be a side plot that runs parallel to the main manga storyline for that period of time.