Yes. It would certainly explain her raging jealousy toward Lily.
As for the thestrals, that bothered me a lot but I think it is subtly explained: In order to see thestrals, one must witness death. I do not think Harry actually saw his parents die. He heard screams and saw a green flash. After witnessing Cedric die, he could see the thestrals. I am also reminded of what Rowling herself has said, and it is quoted somewhere on this thread--that, in a nutshell, dead is dead, even in the wizarding world.
I have long thought that Snape must have had a thing for Lily. So much hatred toward James...that can't be from teenage rivalry alone, can it? He lost the girl.
I really do wonder about how the professors spend their free time. Some of them we know live at the castle, but do they all? Do any of them have families of their own to go home to at night?