My personal opinion on Alyssa:
In season 1 she tells Jack that being in the Order is the only thing she accomplished that is actually hers. In season 2 ep 9, at the pizza place, we see her telling Jack again that all her life she was told what to do. So, basically she was never allowed to make her own decisions and now that she is able to she is trying to make justice for everyone, as in season 1 she tells Lilith “Edward Coventry isn't the bad guy." (because she thought he was doing something that would be good for everyone) and in season 2 she says that “The Praxis is doing everything the Order claims to do." which is helping people.
About she not caring about the explosions killing people, she was considering the theory of the greater good (that there will be sacrifices, herself included after Salvador dies, but ultimately everyone will be able to have access to magic which is her passion, she loves it so much she is willing to die so that everyone can have it).
At the end of season 2, the fact that she took Vera's magic it was an act of revenge since Vera knew all along that her magic was broken because of the Vade Maecum (that she tricked everyone into thinking she had burned it while she actually kept it) and still did nothing about it, quite the opposite started excluding her exactly because of that. All along she was being constantly used and manipulated and ultimately, when she's no longer needed, she's betrayed by the people she admires.
When it comes to Jack, she can be thinking she's not good enough for him (again at the pizza place she told him that people would always tell her she was “not good enough, not pretty enough" and that damaged her) and decides to step back. Or because of those betrayals she's afraid to get to atched to him, as you see as the story develops and they get closer all of a sudden something happens to her and she steps back. I mean I can't blame her for being afraid to get hurt. Still she loves him so much that she chose to protect him by wiping out his memories (knowing if he ever found out he would be extremely mad at her) than let the Order go after him.
Honestly I don't think Alyssa is a bad person, she has actually a good heart. I just think she's wrongfully done a lot of bad choices because people were taking advantage her kindness to manipulate her into doing what they wanted for their personal gain by making her think she was doing what was best for everyone.
Sorry for the very long post.