You know that "on" sometimes means "about":"A conference on English language". And you know that "to" sometimes refers to the direction. Here he wants to change the subject from what he was talking about "to" another subject, and he wants to say something "about" the twins. So he says:"And then on to the twins".
2) Here "to" comes before infinitive. You can also say:
"appearing in the passage once a week was his job".
But the meaning is not exactly the same.
"Oooooh!" and "Aaaah!" are what the character says, they are not infinitives but they are put in quotation mark and used as infinitives.
3) "One night his feet went from under him". I think it just means that he sliped on the stairs. You can imagine what happens before you crash down the stairs, your feet went from under you.
Note that this story is somewhat old and the author might have used English language in an old way.
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