あたり can mean that you were successful at something. In this case though, she was unsuccessful in finding the books she was seeking.
I’m not sure there is a good way to keep the phrasing in English. I think you’d have to change the sentence structure, such as saying “I can’t mentally calm down if I’ve forgotten to thank someone.” I don’t recall (and I can’t seem to find) a ～ずに…ない grammar point, but I could be wrong.
Hmmm, maybe I can go for another attempt. Just in case you can’t imagine what kind of hairpin she wants to use, she wants one of those sticks you can put in your hair after putting it up so that it doesn’t get loose, something like this:
which holds your hair like this:
So basically she just wants a simple cylindrical piece of wood. So, her basic reaction is to look around the house looking for something like that.
The second paragraph explains that the very first thing she finds of this nature is トゥーリ’s doll. The doll’s legs are probably cylindrical and the doll’s made of wood, so it seems to be a perfect fit. So she goes ahead and asks トゥーリ is she can break one of the legs.
Does that help maybe?
So it’s あたり＋は＋なし (as in the は particle), not あたり＋はなし, right? Because はなし can be a suffix, but it didn’t seem to fit. Funny thing is, I originally thought it was 当たり and なし, but I didn’t understand (or maybe forgot) the context, so I couldn’t make sense of the whole phrase until your explanation. Thanks!
I did look up what 簪 look like, but your picture is much clearer than what I had found. The rest of that part made sense from the previous explanation. I was still confused by the final sentence (my bad for not clarifying), but I just read it one more time and I got it now. Thanks again!
Yeah, I definitely could have made that clearer. It is あたり＋は＋なし.
There’s no あたり (correct answer).
I read it as two parts. If I add the optional Japanese comma, it would be:
お礼は忘れずに、しないと精神的に落ち着かない。
I’m mostly thinking that, because young kids around me are often told “お礼は忘れずに” or “ご挨拶は忘れずに”.
In this specific case, it could be a grammar point I don’t about, though, as @icefang97 said.
I took it as a different のに, specifically the last one listed here:
［連語］《準体助詞「の」＋格助詞「に」》
１ …時に。…場合に。「地震が来るのに備えておこう」
２ …のものとして。「儀式用のには不適当だ」
Is there any specific problem you still have with it?
Edit: oh boy, I had to go for a while, and I see a bunch of replies happened in the meantime.
Edit2: oh well, guess everything was cleared while I was away. Good
I presumptuously checked “I’m reading along” and then practically forgot that this book existed until tonight. Oh well, I’ll have some catching up to do I guess.
I also had trouble with a のに. (it is the part after the pleasant pig scene in chapter 4)
しばらくは夢にみそうな光景で、思い出すだけで鳥肌が立つのに、そんなところに行きたくない。
I get the parts… but I’m not sure which of the may のに this one is…
Same. I wonder if it could be the nominalisation の + one of the zillion にs?
A dark thought that has since crossed my mind as well 
Just finished chapter four!
I can totally see マイン overthrowing the nobility just so she can read books.
Reading this book coupled with the fact that I recently got a book called ‘How to invent everything’ which I haven’t started yet but promises to be ‘All the information you need to rebuild civilization’ has made me think I’d be cool to read an 異世界 where a modern genius scientist goes to a world like this and tries to advance technology from scratch. Might be difficult. And probably too unrealistic. But still.
It’s not a novel but have you dipped into Dr. Stone?
This のに here is more like “while” or “whereas”. “Whereas/while no bookstores exist, there’s no way I can get my hands on one.”
Interesting. Do you have any grammar pages you could share that go over that usage?
Don’t know about grammar resources, but dictionaries give while/when/whereas as one of the entries for it.
You didn’t though? 
While I’m commenting anyway, I guess I can add how the discussion in the 1st weeks thread about shuu potentially showing up again confused me. I didn’t get that impression at all. I suppose if he does show up again I’ll be the only one surprised 
I did though. Which part should I blurred more? I blurred what we were talking about
Indeed you did, sorry. 
I was under the impression that de-blurred lines still looked somehow different from not blurred to begin with lines, but apparently they don’t.
Since I just got my 電子辞書 back, I thought it might help people if I transcribed the entry as well. It’s from the Shogakukan Progressive Japanese–English Dictionary:
2「･･･と比べ」while; when
父は背が低いのに母は高い
My mother is tall, while my father is short.
皆が働いているのにどうして遊びに行ける
How can I go and have fun when everybody else is working?
@Redglare directed me here for Honzuki grammar questions 
Sorry for the necro 
I was having some trouble with the section in the 3rd chapter where マイン is describing the walls of the fort/castle part of the town.
白一色で限り気のない壁が続く様子は、見栄えを一番に考えた豪華で装飾的な感じでもないし、砦のような武骨な感じとも少し違う。隔てる意図は感じられても、攻撃されることを想定していないような無防備さに見えるのだ。
This fragment was particularly confusing:
見栄えを一番に考えた豪華で装飾的な感じでもないし
I’m just not understanding how the grammar is fitting together here, but I get the idea that it’s not supposed to be a decorative wall just for show? Something like ‘It wasn’t decorative feeling with the extravagance of the number one thought being of outward appearance’? Maybe it’s just throwing me off how clunky that sounds in English?
Then:
隔てる意図は感じられても
Even if there’s the feeling of intentional separation
攻撃されることを想定していないような無防備さに見えるのだ
if theres not the expectation of there being an attack, it would look defenseless? Did I get that right? It might be the negative in the middle of the sentence that’s throwing me here.
I’ll answer this one quickly because I don’t have to look anything up!
Ugh except I still can’t seem to copy and paste within these boxes.
無防備さに見える is the main clause.
“攻撃されることを想定していない” qualifies that.
So it looked defenseless, as if they weren’t expecting an attack.