The second conversation with Jim Archer is simple. Ask him about the safe deposit key. It's about two and a half seconds faster to say "could this be it?", because if you pick the other option, he responds with "really?" before Nancy shows him the key. He asks you to do a favor, and it's about .1 seconds to say, "Sure!" over "Such as?".
It's about two seconds faster to tell him to get a new seamstress, over asking how much he'll pay. And it's about one second faster to ask how much work needs to be done on the dress, over telling him to say no more.
With the second Jane conversation, you need to pick the second option twice. The first time is faster, because Jane doesn't say "No. You mean...". The second time is faster, because it avoids a conversation about the culprit's motive. When Jane gives you the pie puzzle, it's faster to say "Sounds good!" over "if you insist".
When you find the hidden passageway leading to Emily's room, it triggers a conversation with Jane, the next time you talk to her. It's faster to avoid this conversation, so I talk to Jane (to get the sewing needle) before I find the hidden passageway. Also, good news! You don't have to talk to Topham about the Shakespeare book, before you can explore his house. You can go through the hidden passageway and explore his house directly.