Why was Twilight the one who seemed the most likely to believe Sunset? Because her only memory of her was when Sunset yelled at her after Twilight accidentally brought a monster from Equestria to Canterlot High during the Friendship Games. While it did paint Sunset in a bad light, it would be understandable for Sunset to be yelling at her for misusing magic and possibly hurt somebody, especially after such a stressful event. Therefore, Twilight would probably have thought Sunset was having a bad day and would be her friend again had her other friends not told her about Sunset's past acts.
At the end of the special, Wallflower admits to having used the Memory Stone, to erase awkward hellos and other embarrassing moments from everyone else's memories. Her overuse of the stone is the reason why no one could ever remember her.
A bit of Fridge Funny with Sunset during the climax. She just lost all of her memories and as far she knows, she's a pony now stuck in a strange body and an even stranger world. That's heartbreaking. Her terror, however, would be quickly replaced with confusion as she pony ups with the other girls and more and more confusing things happen to the point she's just going along with the other girls.
Sunset gets to empathise better with Wallflower's pain because when she saw Wallflower's memories, it was mostly her standing alone while everybody else had fun around her. The scenes would be the exact same if Wallflower were removed from them... just like Applejack's memories where Sunset saw herself erased and the scene moving on as if she didn't exist.
Sunset acts surprised when Princess Celestia takes her to the restricted section, but not as excited as Twilight. Of course, Twilight overreacts to anything related to books. But it may also be because, unlike Twilight who didn't know it existed, Sunset's past attitude means she's probably already seen it.
Sunset's surprised that Celestia has a sense of humor. This isn't because Celestia didn't have a sense of humor back then, but because Sunset was too much of a Spoiled Brat at the time to see or appreciate it.
Sunset treating Princess Luna normally instead of outright terror of the pony who used to be Nightmare Moon may be because of her experience interacting with Vice-Principal Luna, which would only fuel her laughter at the contrast between the two.
Similarly, Princess Luna shows no hostility to Sunset because she never met her pre-HeelFace Turn.
When the characters first got their geodes and discovered the powers associated with them, Sunset Shimmer's powers may have seemed like a random choice (telepathy, usually requiring physical contact), but then in this program it turned out to be a very useful item when it was used to counter the memory loss stone. The writing staff planned this all along!
Wallflower Blush is a case of Remember the New Guy?...but think about it. Her entire schtick is that no one ever seems to notice she exists until she talks to them and says she was at X event. In other words, she actually was there all along...except none of us noticed her!
Wallflower blurts out that she erased Sunset's memories while next to the main cast. A simple case of Saying Too Much — but it could have been caused by the fact that, since she's always gone unnoticed, she's grown used to people not paying attention to her when she speaks and didn't think blurting this out was a bad idea.
Also, ironically: the person who's been constantly ignored is undone because she ignored who was sitting nearby.
Wallflower Blush didn't turn into a monster like Sunset, Twilight, Gloriosa, or Juniper when using magic but this could be because unlike them, she wasn't using the magic of the Elements of Harmony. She was only using the natural magic of the Memory Stone, which had no connections whatsoever to the Elements of Harmony and definitely far less powerful. Thus it is probably easier to control but still dangerous. It's likely that if Wallflower continued to use the Memory Stone after removing Sunset's memory of the human world, she would have turned into a monster like the other girls.
Sunset calling Trixie a blowhard instead of the other word is likely because she's currently in school and yelling a swear like that at another student would definitely have gotten Sunset in trouble and waste time.
Sunset turning off the lights while Wallflower is still in the room (despite speaking to her just moments ago) may seem a little harsh, unless you take into account Wallflower's later statement that she'd been using the Memory Stone to erase awkward meetings from the minds of others. Since her and Sunset's conversation was mostly about how Sunset didn't remember their first meeting years ago, or that Wallflower was even part of the committee, Wallflower may have secretly erased the memory of that awkward talk from Sunset and the others' minds when they weren't looking.
Some might take issue with how Wallflower Blush seemingly got off Scott free and wasn't arrested or something similar. Keep in mind that she was constantly ignored by others for years, thus she wouldn't exactly be in a good state of mind. She just wanted some company, and a place like prison would not be a good place to go about making friends, especially in her state. That's why everyone decided to help her out.
How was Trixie able to use stage-magic to escape a locked room via teleportation? Let's look at the scene in context. Sunset tells her that even if she fails to restore the memory of her other friends, she will still have a friend in Trixie, who is the "Greatest and Powerful-est" in CHS. It's obviously the Magic of Friendship at work. note We could assume she had a dormant magic leak in her, but that would cross into WMG territory.
In an example of Heartwarming in Hindsight, Princess Celestia's wish for Sunset to return to Equestria seeking guidance from the first movie has finally come true.
The mere fact that Wallflower Blush wasn't corrupted by magic and turned into a monster. It means that everything she did, erasing all the good memories of Sunset and later trying to erase the Mane Seven's memories of each other, was done entirely by her own free will, desperate and naive as that free will was (it's clear once she sees it happen in front of her that she hadn't realized just how traumatic the effects of the magic would be, as Twilight states she was using magic she didn't understand).
If the girls hadn't restored Sunset's memories right after she lost them, not only would it mean that Sunset would have to relearn how to be a human again but she would truly turn back into the mean and tyrannical Sunset she used to be. She might even decide to go back to Equestria and try to steal the Element of Magic (or all of the Elements of Harmony since they're currently in the Tree of Harmony) again.
That assumes everything goes back to normal. It's possible with the correct influences she'd have been guided in another direction. The Sunset everyone knew, however, would be mostly gone.
The fact she could still use her friendship powers shows that she still understands friendship. Her character development was not lost, just her memories of the human world. It was just like how her friends still had their growth, just without Sunset (even though plenty of things make no sense in that regard). Also, sadly, she would likely end up just going back to Equestria if her memories were not restored; she did think she was still Celestia's student based on her dialog.
Looks like Starswirl isn't the only pony who uses the human world as a dumping ground for dangerous villains and artifacts...
So like teacher, like student?
The girls comparing Wallflower to Fluttershy gets a little more heartbreaking when you realize Fluttershy could have easily become like Wallflower due to her shyness and tendency for people to walk past her. She would have become desperately lonely just like Wallflower, with only her animals for company, if Princess Twilight didn't go to the human world and help repair the Mane Five's friendships.
The students probably remember Sunset turning into a demon and trying to brainwash them into being her army. They wouldn't forgive Sunset, especially if their memories show that she didn't even try to be good after turning into a literal monster. Now look at Human Twilight. She was turned into a monster like Sunset by magic but the moment she turned back to normal, the whole school forgave her near instantly. It would be more painful for Sunset to realize that the school forgave Twilight for Midnight's actions but kept holding Demon Sunset's action against her.
Except Twilight's situation was different in some important ways, she outright yells "Help me!" right before she transforms (a more blatant sign that she didn't want this, compared to Sunset's silent tears when she transformed), and even in the altered memories the first thing she does after changing back is apologize.
Watching the Mane Six have fun without Sunset can make one realize that this is what was supposed to be the human worlds natural course before Sunset came and introduced Equestrian magic to a world that had very little, if any, natural magic of its own. Sunset Shimmer was never supposed to become best friends with the Mane Six or even be a part of the human world.