I don't think those unanswered questions were all that unanswered, btw. The answer to many of them was implied.
1. Is it true that Yuko and Kenji used to have a relationship?
It's implied, but never stated outright. The devs could have stated it definitely, but it's obvious they chose not to. Sometimes leaving stuff to the imagination is better than spelling out EVERYTHING. Often, good works of fiction create worlds where there's enough unsaid for fans to start speculation and discussion, rather than worlds where EVERYTHING about characters is spelled out.
2. What was the root of Lily and Shizune’s strife?
Personality differences. They used to get along until Shizune became student council president and were forced to work together in that dynamic.Shizune is brash, impatient, impulsive, confrontational and ambitious. Lilly is laid-back, careful, easy going, patient and avoids confrontations. Given that they've known each other for a long time, their inability to work together productively took on a personal element.
3. Misha’s hair, how did she came up with such an idea. And did she choose it before or after Lily and Shizune fought?
Lilly and Shizune have nothing to do with that. Misha changed her hair style after she confessed to Shizune and was turned down. A hairstyle change for a woman is sometimes seen as a sign of being spurned by a loved one in Japan. Why so radical? No idea. Maybe she just likes it...same with the T-shirt. It fits with her loud personality.
4. How was Hanako doing in the 3 years before Lily came to board? (She never met Lily until 3rd year)
Actually, they met somewhere around the second year. How Hanako was doing before she met Lilly? Pretty much how she was doing since her accident...except she wasn't bullied anymore at Yamaku. Most people who knew who she was stopped trying to talk to her a long time ago. Hanako's life was pretty much spent inside her dorm room or her little corner in the library and consisted of trying to avoid as much social interaction as humanly possible.
5. How does Hanako sings? (Lily said Hanako is a singer)
The same way everybody sings.
6. How did Hanako and Lily’s relationship came to be
After Lilly moved into the room next to her, Hanako overheard Lilly comforting a classmate. Feeling lonely herself, Hanako eventually visited Lilly in her room. At first, Hanako was too shy to even talk to Lilly and her visits were completely spent with Lilly talking and Hanako listening. Eventually she worked up the courage to start conversations with her. The rest is history.
7. How does Rin and Emi managed to adapt to each others differences?
You mean personality differences? They didn't need to adapt. Given their own issues, Rin and Emi are perfectly "safe" friends for each other. For Emi, Rin is safe because she knows Rin is happy to hang out with her and whenever her traumatic experiences start clouding her mood, she knows Rin will either be unwilling or unable to dig into her past. For Rin, Emi is safe because Emi prefers relatively shallow human relationships and thus isn't bothered that she can't communicate with Rin on a deeper level.
Only the normal people believes that special people needs special attention. Just look at how Lily, Hanako, Shizune, Emi, Rin, Meiko and so many other characters can live with their disfigurements. Had they ever tried to blame their differences for not being able to live a good life?
NO!
I suppose you meant Miki instead of Meiko, right?
Hanako and Emi definitely feel resentful about their condition in their own way. Hanako states outright she's happy she was able to come to Yamaku because it's become a place for her to belong (to some degree) and she's at least not bullied here anymore. And the special attention consists of an on-campus nursing staff, physical and mental therapy department and many other little adjustments to allow the students to focus more on their study and less on day-to-day coping with their condition.