On page 95, when told that Yotsuba has something to say to Fuuka, Asagi responds with
でも風香 今 出かけてていないわよ
Which is supposed to mean that she isn’t home right now, I guess. Ichi.moe says 出かけてていない is actually 出かけて + いて + いない.
But why the double いる? And why is she negating 出かける?
I’m drawing a blank right now.
On Page 98, Asagi told Yotsuba
夏でもすずしくしてしまう機械よ
夏でも(In the summer also)
すずしく(Refreshing) Why we attached く？
してしまう(?) As I understood from Tae Kim book, it’s used for unintended actions but it does not make sense to me here
機械(Machine)
It’s also a machine that makes you cool in the summer かな
I think ichi.moe is confused in this case. What do you make of it if you read it like this?
「出かけてて、いないわよ」
すずしい = adjective = modifies a noun
すずしく = adverb = modifies a verb
I think “adverb + する” means “to make it be (adverb)”. For example, すずしくする I think means “to make it be cool (temperature)”.
This can be for unintended actions, but it can also be used for completed actions.
すずしく + して + しまう = completely make it cool
(I could be wrong about the specific nuance. I’m still learning how to understand しまう.)
Here, I would translate でも as “even”. “Even in the summer…”
「夏でもすずしくしてしまう機械よ」
“It’s a machine that makes it completely cool, even in the summer.”
O right, so more like ‘She’s gone off, she isn’t here’.
That’s my understanding based on some web searches of the multiple て’s. It probably doesn’t make sense to string いる and いる together after another verb, and the various forum results I stumbled across seemed to suggest as much.
The parser program mecab seems to agree with this. Here’s the output I get (translated into English):
| Input | Part of Speech |
|---|---|
| 出かけ | verb (independent) |
| て | verb (dependent) |
| て | conjunction particle |
| い | verb (dependent) |
| ない | auxiliary verb |
I was thinking about this, but there’s no pause when she speaks.
There’s usually an indication.
Might be it, though. What do I know.
て is a “conjunction particle”…??? I don’t think I’ve ever seen that before!
But from what you are saying, it seems that it is not an actual particle, but a shortened いて, ie：
出かける - to go out, put into て-form in order to connect it to another verb 
出かけて
Plus いる, to make continuous state 出かけている
This is then also put into て-form to connect it to another verb 出かけていて
Then the い is dropped (because the sentence is getting too long!) 出かけてて
Then いる in the negative (いない) is added 出かけてていない
So the て-conjunction particle is essentially the て-form with the い dropped? Does that sound right?
Thank you @nienque for asking this one, thank you @ChristopherFritz, for your answer, and thank you anyone who can tell me if I’m still going wrong somewhere! 
Your list of steps to turn 出かける + いる + いる + ない into 出かけてていない looks the same as I break it down to be.
The Japanese name for it is 接続助詞.
The 助詞 part is what we call “particle” (see WaniKani level 19 entry; it’s okay to peek ahead). It’s 助 (help) + level 19’s 詞 (part of speech).
The 接続 portion is “connection” or “conjunction” or “join” or “link”. (Maybe I should stat calling it the “linking particle” because that’s a more simple of these words. I like using simple words for grammar stuffs.) This word isn’t in WaniKani, but the kanji are level 26’s 接 (adjoin) + level 19’s 続 (continue). It makes sense, right? You adjoin and continue, attaching one verb to another to continue a series of actions. And this attaching is done with a “linking particle” (or “conjunction particle”).
I decided to put the dropped い in and see what mecab says, and now it’s changed the first て (verb) in my prior post to い (verb) + て (linking particle)… 
(my first time ever using this icon)
| Input | Part of Speech |
|---|---|
| 出かけ | verb (independent) |
| て | conjunction particle |
| い | verb (dependent) |
| て | conjunction particle |
| い | verb (dependent) |
| ない | auxiliary verb |
Wow, that is brilliant! Thank you again so much @ChristopherFritz!
Another question, this time about page 110. After Yotsuba discovers her father is an ‘enemy of the earrth’ (lol), Ena tries to comfort her. She says:
クーラーはすずしくってとってもいいなぁ
Is すずしくって just a somewhat more staccato て-form of すずしい? Like how とても becomes とっても? Or is it an adverb combined with って?
Page 110
Good question. I wish I knew the answer!
クーラーは - the air-con + は
すずしくって -
とっても - very. (This is a perfectly legit. form of てても, but it makes me wonder if Ena likes to stick in the little っ as often as she can?!)
いい - good
なぁ - sentence ending particle
So, to me it looks like she’s saying “The air-con is refreshing and very good”, ie the て-form.
But I suppose it could be って as “if…then”… “if the air-con is refreshing, then that’s very good, right?” I have no idea!
I’d say it’s the quoting version of って or と.
The fact that “the cooler (air conditioner) is pretty cool (refreshing)” is very good, right?
Then she goes on to talk about how it consumes less energy than usual and is less harmful for the Earth.
She’s basically introducing a new topic (or opinion) in an attempt to pivot the conversation.
Yeah? 
Omg now that you mention it that makes so much sense lol
Why would it be an adverb though, and not an adjective or verb? Why not すずしい for example?
I think the すずしく implies that you’re omitting する, and then maybe the sentence is trailing off a bit.
I’m not exactly sure about it, but that’s how I interpret it.
I also think I made a mistake earlier, and it’s not exactly the quoting use of って, but it’s being used in place of the 「は」 particle to simply bring up a topic.
Ha, it’s funny how both the って＝と and the って＝は interpretation lead to the same fundamental meaning:
It shows that your intuition was on point 
On page 135 there’s Fuuka’s mum saying:
もってっちゃって邪魔だから
I guess she’s saying that they’re welcome to take the television, cause it was just getting in the way. But how does it work? I recognise もって (from 持つ I imagine) and ちゃって (for something that is finished, or unfortunate). But why the っ in between the two…?
I think it’s short for もっていっちゃってー持って＋行って＋しまって
So they’re supposed to take it with them, not just carry it.
It looks like ichi.moe agrees:
