Apparently, if we are to trust this random blogspot site I found:
適当 Tekitou: This is a word that can have a good or bad meaning depending on the context and the values of the person using it. If it’s used in the negative sense, it can mean something like vague, unserious, or half-assed. In a positive way, it can be used to describe something done casually, quickly and without too much effort or stress. Relaxed or lazy, depending on the context.
Dictionaries say it means “Appropriate”, but the English translation of the chapter further convinces me of this approach. "お前テキトーな事言うなよ” becomes “Don’t say vague/half-assed things” (about not knowing what Water World is.)
Or perhaps it’s just “Don’t say appropriate stuff like that” (about Yotsuba usually being more random or exaggerated in her speech and mannerisms.)
Couldn’t find anything about ダシ. 
As @BobaGakusei said, on the vocabulary list 出し is explained as Pretext.
引っ込む: to withdraw (e.g. from the public eye), to retire to (somewhere), to stay indoors, to butt out, to stay out of it. “Children should stay out if it!”
私ねー is pretty common (said by kids) from my experience, something like: “You know, I…”
Even though she has a little too much meat around the waist, that’s fine with a lot of people. (Or, there are people (maniacs/enthusiasts) that like it that way.) マニアックで良い.
And yes, it should be Ena saying that. 
A really fun chapter as always! If not for your questions I wouldn’t have paid much attention. 
Fuuka cover on the next one. 