I initially thought of Amity as a mean rich girl who bullies everyone, including Willow; however, as the series went on, I didn't see her as such, and after watching episodes beginning with "Lost in Language" and ending with "Understanding Willow", it all made WAY TOO MUCH sense on who she REALLY is and WHY she behaved the way she did:
Amity has a complex trauma (C-PTSD) from her upbringing; she was emotionally abused by Odalia, emotionally neglected by Alador who enables Odalia's abusive behavior, and even teased and pushed away by Emira and Edric. Because of that, Amity was raised as a miserable loner with no love or respect, and under Odalia's influence, she had been living a lie and putting on an act and façade (such as being bully, faking her desire of joining the coven which was forced upon by Odalia, associating with Boscha and her gang which was also forced upon by Odalia, etc).
Both "Lost in Language" and "Understanding Willow" made crystal clear without a shadow of a doubt that Amity was NEVER a bully she appeared to be; her selfish and harsh behavior was simply a reaction to how she was treated as a child, as well as her coping with not only her childhood trauma she had endured in years, but also her loneliness and misery as a result of Odalia forcing her to end her friendship with Willow. She never wanted to hurt Willow and was forced to do so; she was just pretending to dislike Willow and acting as a bully to protect her from Odalia and that's all. Compared with her favorite children's book character Odiban; Amity never had real friends and her friendship with Willow was forcefully cut off by Odalia, who bullied her into associating with Boscha, who was a real bully. She never considered Boscha and her gang as her real friends and never called them "her friends" at all. Odalia compelled Amity to get green hair because she wanted her children to be "color coordinated", despite the fact that Amity inherited her father Alador's hair color. All she wanted was love, respect, and a real friends who she can laugh with and grow together with, but they keep being taken away.
And here's more, Amity never wanted to join the Emperor's Coven; her seeming excitement to join it was, IN FACT, forced upon her by Odalia. Amity also hoped that if she will have to participate in something she dislikes, she might as well try to get something out of it for herself such as love and respect from her family and the others. Amity was expecting for a better future since, according to her sister Emira, the former wasn't happy in the past and it wasn't denied by Amity who was looking for a future that would make her happy, which ironically wouldn't have happened at all.
But when Luz came around (despite taking some time), Amity finally began to come out of the shell that Odalia forced her in and Amity became a better person for it.
And besides that, Amity DID deserve to be mean to Luz from the beginning, even if she wasn't ACTUALLY bullying her; she was just VERY ANGRY at her for helping Willow cheat and getting her in trouble at school. As for King, she was only mean to him by association because he knew Luz.
Amity DIDN'T try to dissect Luz. She was just trying to force Luz into revealing she wasn't an abomination. What she wanted was to prove Willow cheated. Luz wasn't tied up or anything, if she didn't want to get stabbed all she had to do was... move out of the way.
Amity never had any social life after what happened with Willow, she couldn't stand Boscha and her gang and didn't have any actual friends; she only hung out with them superficially (it means fakely) under Odalia's influence. Once Luz befriended her, Amity's life got a million times better and she was actually happy for the first time in literal years.
Same as the one with Luz, Amity didn't wanted Boscha and her gang to find out about her true friendship with Willow, so she tried to burn the photo memory of their childhood friendship.
While in Willow's mind, the real reason Amity didn't wanted to fix the memory of her friendship with Willow is that she didn't want Luz to find out, because she was afraid Luz would judge her especially without the proper context and thought she'd end up losing another real friend.
However, thanks to Luz's emotional support, Amity reconciled with Willow by explaining the whole situation and ended her forced association with Boscha and her gang in Understanding Willow; they became friends again in Wing it Like Witches which chronologically takes place either a few weeks or maybe one month after Enchanting Grom Fright. Despite fixing everything and regaining her friendship with Willow who understood and forgave her, Amity still felt bad about what happened, both the part with Odalia and the fact that she almost burned up Willow's brain trying to hide it, she knows Willow isn't angry anymore, but she still felt bad that all that stuff still happened because she was afraid to let Luz and Willow know the truth.