1) It was probably one of those "let the villain go and maybe she'll see the errors of her ways" situation.
2) She probably didn't expect the revenge from Starlight until the beginning of the first part.
3) Twilight felt safe in Ponyville, so she felt no need to have extra security. In the first part, she even said "This is Ponyville. How bad could things be?"
4) I don't know about this one. It's always those things in movies or shows where the protagonist doesn't act right away and wait for things to unfold. After all, Twilight isn't too bright in these kinds of situations.
5) No one ever kills in Equestria (at least in that timeline). Also, even if Twilight did want to, we later learned that Starlight is probably almost (if not as) strong as Twilight in magic, despite Twilgiht being an Alicorn.
To be honest, my main complaint is that after Twilgiht JUST
They didn't put out a wanted list for her because it was probably one of those "let the villain go and maybe she'll see the error of her ways" thing.
Well, most of the explanation for those is that it's wrong to kill. And even if Twilight wanted to waste Starlight, their magic powers are equal in strength (or at least, very close).
As for not having security, Twilight felt safe in Ponyville, which is why she didn't have any security in her castle. ("This is Ponyville. How bad can things be?")
My main complaint is that after Twilight JUST had a lecture about how important Rainbow Dash's Sonic Rainboom was, and after realizing they went back in time to that very moment, she had no idea what Starlight glimmer was planning.