|Fig. 1: 此頃目見え|
"It was a shitajikko (this is an abbreviation for a child being trained as a geisha), who has been recently coming for meetings with me (fig. 1)."The most interesting feature of this sentence is the use of parallel lines that I previously thought were reserved for togaki （ト書き） for a parenthetical explanation. That is, the parenthetical sentence above is not a gloss that I added ― it was included by Tamenaga, for clarification.
Presumably, the term shitajikko (written as 「下地っ子」 in modern Japanese), meaning "young boy or girl being trained as a geisha or as a kabuki actor", wasn't one that the average reader would be familiar with. Since Yonehachi is a geisha herself, we can assume that it's referring to a young girl being trained by her.
Edit: Matt's comment here explained the grammar for the end of the sentence in fig. 1. 「ありまはアな」 is a form of 「あります」 where 「ます」 has first been modified to the geisha-specific form 「まふ」, and then 「まはあ」 is a sound-shifted form of 「まふ」, similar to the transformation that resulted in 「まさア」 in fig. 1 of this post.
The use of the humble word 「目見え」 to refer to the meetings between Yonehachi and the shitajikko shows the difference in their ranks ― Yonehachi is a full-fledged geisha, which puts her in a position of superiority with respect to her student.
|Fig. 2: その|
"When I asked the girl where her house was, she said it was in Honjou (fig. 2), and so while talking and having a good time with everyone (fig. 3), when that girl was talking about her neighborhood (fig. 4), the circumstances of the conversation became gossip about you (fig. 5)."
This is the first time we're encountering the conjunctive particle 「ば」, in 「聞たれば」 (outside of the kotowaza 「住めば都」). Note that the particle's meaning changes based upon the form of the verb preceding it. If the verb is in the imperfective form （未然形）, then it takes on a hypothetical (if X, then Y) meaning. But in this case, it follows the realis form （已然形）, meaning it implies a logical connection (i.e., "when").
|Fig. 3: それから皆々|
|Fig. 4: 其子が宅|
I'm not sure about the kanji for 「あそ」, since the kuzushiji version doesn't look anything like 「遊」. I couldn't find any kanji that had a similar meaning or reading, but the meaning of the word itself is quite clear.
In fig. 4, you can see a nonstandard kanji for 「はなし」, namely 「咄]. The kuzushiji form of 「近」 is interesting because it seems to have entirely dropped the "advance" radical （之繞）, or 「辶」. Also note how the kuzushiji form of 「所」 here is entirely different from the one observed in fig. 2, in 「本所」.
|Fig. 5: どふも|
Note the unusual kanji choice for the kuzushiji form of 「す」 in the furigana for 「様子」 ― the most common one is 「寸」, which is the origin of the modern hiragana 「す」. I was able to decpiher the kanji, as we have seen 「様」 in Umegoyomi several times before, and 「子」 was quite straightforward too. But without the kanji, it would have been easy to overlook the squiggle at the top of 「す」 and think it was actually 「て」.
|Fig. 6: 其の晩|
In fig. 6, once again we see the use of a modern verb ― 「寝かす」, as this sentence takes places within a character's dialogue.
The first thing to note about fig. 7 is the use of the word 「意気」 ― although its literal meaning is heart/spirit, it seemed to me that Yonehachi was primarily referring to the wife's appearance.
|Fig. 7: 宅に意気|
|Fig. 8: 夫じや|
|Fig. 9: 猶くわ|
The word 「くわしく」 would be grammatically valid according to either premodern or modern Japanese rules. In premodern Japanese, the continuative form （連用形） of the adjective 「くわし」 is also 「くわしく」, with the primary distinction being in the dictionary forms, where the premodern version doesn't end with an 「い」 (thus「くわし」, instead of 「くわしい」).
|Fig. 10: おまはん|
I have to say, this dialogue is much easier to understand and follow than the narration. It's almost as if two different languages are in use. After transcribing the kuzushiji into typewritten kanji/kana, reading the dialogue is quite similar to reading modern Japanese.