A few questions about TSRfST [Spoilers]

I'm just done reading it for the first time and I'm not a native, so sorry if my questions cover very obvious topics, but those came to my mind after being done:

a) Why does she (seemingly) randomly start to cry/weep at multiple times? To show her broken personality?

b) What is implied on multiple occassions when she get's an urge or a desire and she tries to suppress it? I don't know if I'm too dumb to realize or if it's kind of hidden

c) Who's Esther?

d) On Day 2 or 3 she starts to panic and runs back, did I miss the reason or why did she run back and/or panicked? I didn't understand it :D

e) Any tips/hints why she seems to be a good alchemist and namer? Is it seen as confirmed that she was at the university at some point (I've read the theory with Auri being Aurielle and studying under a fake name)

f) Does someone else sometimes have the feeling Auri is evil/acts sinister? Maybe I'm misinterpreting but on the last page of the second last chapter, it says: "He would need a place someday, and it was here all ready for him. Someday he would come, and she would tend to him. Someday he would be the one all eggshell hollow empty in the dark. [...] She would call up all her cunning and her craft. Then she would make a name for him.". I don't know, sometime that seems rather dark to me and she means Kote the innkeeper with the hollow egg shell?

Thanks everyone for answering and happy waiting for book 3 :D