That’s N3 grammar! 
Although we did learn it for the N4. (I forgot 
)
It’s connected to 大きくなったねぇー, so it’s basically:
“You grew up while I wasn’t looking.” 
兄みたいなもの or 兄みたいなもん is “something like a brother”.
“I’m something like a brother to Yotsuba.”
The で could be a contraction of です.
Otherwise, Jisho.org: Japanese Dictionary by itself seems to be “because”, but not only does it not make sense in context, it also leaves 兄みたいな by itself. 
So I don’t think that’s right.
Laughing in a library is fine (with moderation)!
No one can expect you to read Yotsuba with a straight face. 
Let me present my hypothesis:
のり = seaweed
のりのり = in high spirits
つくだに = small seafood, meat or seaweed that has been simmered in soy sauce and mirin.
So, Ena said, “You’re in high spirits, huh?”
Yotsuba doesn’t know what that means, so she only heard のり, and replied with, “Are you talking about preserved food (seaweed)? ”
Then Dad says, “It means that you’re full of energy.” Going back to のりのり.
Then, Yotsuba says, “It’s because of the happi! This is a happi.” (explaining why she’s in a good mood).
Then, Ena does a bilingual pun, and goes, “Because of the happi, you’re happy.”
And Yotsuba goes, “What!?” (I think implying that she thinks there actually is a relation between the two).
Then Ena says, “I was joking (lying).”
Oof, that one was just a little tough to parse.
Great question! Your translation is basically right, but you can afford a few extra words to better convey the message. 
The online translation is basically the same, but I don’t necessarily agree with their exact translation.
Perhaps someone else 
could say what they think.
This time, it seems like it’s 引っ張っていくの, the opposite of 引っ張ってくるの.
If it was くる, it’d be ひっぱってくんの at least.
Since they’re taking instead of bringing(, perhaps?)
Haha! Yotsuba asks what a 山車 is, and her Dad answers:
山車ってのはなぁ…
“A 山車 is…” then explains it.
ってのは is a contraction of Jisho.org: Japanese Dictionary
A more explained translation would be something like, “If you’re talking about a 山車, it’s…”
そういうこと is “That’s it.”, usually from a position of knowledge, while そういうことか is “So that’s it.”, or “I see.”, or “I got it.” with a connotation of barely having learned or understood something.
This one’s also a little tricky, but simple.
So, させる is to make someone do something, but it can also be let someone do something.
In this case, Yotsuba is asking the guy hitting the drums to make her (let her) do it.
させてください (or whatever other verb you put in the beginning in that form) is a way of asking someone to let you do something.
Then 風香 comes to save the day. 
Thank you for the N4 grammar review. 
