I believe it’s said by her father, just following the pattern of how speech bubbles work in other panels. It seems if the character speaking isnt in the panel it doesn’t have any indicator, while if they are present it does. If you notice in the same panel the bubble with おつ has the indicator. So it follows that the other is her father.
Edit;: The exception seeming to be Yotsuba’s exclamations, but those are marked by jaggy lines.
And a very different font. Which I found hard to read for the first chapter and a half.
I considered the panel thing, but he is in there, just way in the back. But it does make sense that it’s just a continuation or he was effectively treated as out-of-frame. What I didn’t consider is that this is literally the first page with dialogue, so it makes sense to establish who she is at that point.
I also thought it’s her father who says her name. In the previous panel he says something to her (“real soon now”) and she doesn’t react, so he calls her by her name to gain her attention. But maybe I’m over-interpreting here.
On page 11, first panel, Yotsuba says “やめろ” (= “stop”) to make Jambo stop shaking her head. On the next panel, her father says "ヤンダは？ まだ？” (I think this means “Stopped? Already?”) - so far so well. But why is the first word written in Katakana? Does this have a special meaning?
Katakana is often used for emphasis, the same way we’d write things in italics. You might also (rarely) see it used to delineate word-boundaries in hiragana-heavy passages.
ヤンダ, though, is someone’s name: Jumbo responds with あーあいつ, “oh, that person”. 「ヤンダは？まだ？」 ~= “What about Yanda? Not [here] yet?”
I believe ヤンダ there is actually a name. Like, “And Yanda?” This is because the next panel his friend ジャンボ says something like, “That person had business come up. That person is no good.”
Ah, that explains a lot, thanks!
I’m still struggling with the whole conversation, so this was an important bit 
I have a question about the use of ぞー.
What is it adding to the meaning of the sentence？
for example the father said "お店もあるぞー”
there are also stores?
The exchange between Jumbo and Yotsuba’s father is the hardest thing you’ll see for a while. Don’t worry if you don’t understand all of it: it really just establishes who Jumbo is and the company the father keeps.
ぞ is kinda like the sentence-ending よ, if you’re familiar with that. It just sounds “cooler”. Sound it out as you read; put dumb, goofy emphasis on it.
So on page 13, the first panel, Jumbo says: んじゃ見つけたらひろっとくわ. Part if that, if I understand correctly, is “Then, if I find her…”, But what is ひろっとくわ？
Also as a side note, does Yotsuba’s father not seem super chill about her vanishing? Even later with the girl on the bike it seems he downplays it while the girl gets alarmed on finding out and goes to look.for her. Just seemed odd to me, but then he seems a little flakey.
ひろっとく is probably 拾っとく, where the kanji means “pick up”, like literally picking something up and taking it. The implication being that, if he finds her, he’ll bring her home. I don’t know what the わ is. Maybe just how Jumbo talks.
And, yeah, father ain’t care and Yotsuba does what she wants. The way the adventures unfold wouldn’t be nearly as fun if he weren’t aloof.
ひろっとくわ is from 拾っておくわ which means “I’ll pick it up” though with the context he seem to mean like “right, I’ll pick them up if I find”
And I think the idea is that Yotsuba is just super quirky and all who know her have just gotten used to her, including especially I guess her father who is used to her wandering off.
PS Bear in mind that Japan is generally a much ‘safer’ place for kids to be wandering alone. It used to blow my mind that young kids of 5 and 6 would walk to my language school alone, crossing many roads to do so. They simply stop by the roadside, raise their hands and the cars stop to let them cross.
Ah got you! I feel kind of dumb, since I realized とく was ておく in a previous panel but not here. Must be because I was unfamiliar with the verb lol! Thanks
I see what you guys mean, especially with the fact in Japan it’s more common to let kids go places in their own. I remember taking a local train into Nagasaki from Omura and being shocked at super young kids being “seen off” at the station by their parents but getting on the train alone. The contrast between his and others’ reactions seemed oddthough! I guess he’d be quite us to it, as you mention.
Possibly the dumbest question, but… I got stuck literally at the chapter title. I understand “よつばと” , but I don’t understand “ひっにし”. Google translate says it’s “easily”, but… I don’t know if that’s right, shouldn’t it have something to do with the fact that the chapter is about moving? Sorry if this has already been resolved somewhere…
It’s actually ひっこし which means moving! Its the stem of 引っ越します which is to move. The font can be a little difficult at times here!
Ahhh thanks so much!!
On page 8 in the third panel, her dad says 俺の分. I assume he’s talking about why he can’t wave, here (saying something along the lines of “my hands are busy”, but 分 means ‘part’ or ‘minute’. What is it doing here?
Yotsuba also says 手えふった. What is the え for?
(And another small one, her dad says ふってくれ. I’m pretty sure I’ve learned this somewhere and I’m being an idiot, but what is the くれ?)
It’s pretty close to the English literal equivalent: “my part”; in this case, “do my share of waving for me”.
That’s a small ぇ. It’s hard to tell with the font, but it’s not left-aligned. 震える (ふるえる, to shake) is the verb she’s trying to use, so it could be that she’s just struggling to position all the sounds, or maybe she’s just holding the vowel out of excitement. [Edit: @rodrigowaick mentioned the correct verb below]
It’s one of the “giving”/“receiving” things: Giving and Receiving - Tae Kim's Japanese grammar guide
I think the verb is actually 振る (ふる) - to wave.
誰に手を振る - to wave at someone