Pg 39 panel 4:
I think this is 吐く - to vomit, actually. Bocchi looks really uncomfortable and nauseous in this panel, after all, like she’s going to throw up from stress. You’re right that Xな means “don’t X”, but all the よ does is add emphasis. So the translation would be “Don’t vomit!” (corrected thanks to @Belthazar and @seanblue)
Pg 41 panel 6: I had to look this one up, I’d never seen it before. あざす is short for ありがとうがぞあいます, yeah. It’s slang, apparently. I would guess Bocchi went for the short slang term because she was too flustered to say ありがとうがぞあいます properly.
Pg 44 panel 4:
Pretty sure this is actually 残念っぷり where っぷり means style/manner/way. If you look closely the っ is smaller than the hiragana below it and.
As for Pg 43 panel 7 I don’t know what’s going on there either (on top of つい, I’m not sure why there’s double たら), so hopefully someone can help the both of us!
Nah, it’s not a contraction, it’s just a negative ending on its own. (~なさい means do do the thing - it’s the ます-form imperative ending. There is a な that’s a contraction of なさい, but like なさい it’s also an order to do the thing, and it also comes after the ます-stem (i.e. 吐きな) rather than the dictionary form as it is here (吐くな).)
I asked for help on another forum regarding page 43.
Page 43
It looks like the first ったら is a conditional and the second one is is a temporal.
So it’s something like “when I thought ‘if it is was mean spirited…’ I just acted without thinking”
Well, it was a bit tricky but I’m basically done for this week. Some points remain obscure, but I feel I understood well enough.
What is she saying at the end ? Some thing like “after the things you’ve said to me, this (them telling her she’s nice and cute) don’t make me particularly happy” ?
The twist being that, indeed, she does like that them come and apologize.