1. Paul seems to have liked to have a missionary partner (Barnabas/Silas) and an assistant or two. Did he use people like John Mark, Titus, and Timothy as work horses? ...
It is fascinating that Acts never mentions Titus...
Why did Paul circumcise Timothy? Had he not fully worked out his theology of justification by faith yet? Did he do it as a shrewd mission strategy? Did he have Titus as his go-between with non-Jews and want Timothy as a go-between with Jews? Timothy's mother was Jewish. By the later reckoning of Jewish tradition, that qualified him as a Jew, even though his father was Greek.
2. Paul and Silas' path probably followed the Roman roads. His sense that they were not to go north or south basically aligns with the cross-road options on the way northwest throughout Asia Minor.
3. The "we" passages of Acts begin at Troas. Traditionally Luke is thought to be the author, the only ancient name suggested. It seems like the author was someone who traveled with Paul a little. The author is with Paul at the end of Acts in Rome. Since Colossians is traditionally dated to that time, the list of people at the end of Colossians does have Luke's name there. Other possibilities of course.
Not a matter of faith... People get upset because so much of their faith has calcified around traditions about the Bible (which includes inerrancy, by the way) rather than the Bible itself.
4. Why did Paul sense there would be some Jews worshiping by the river? Some clever speculations pop up here. One I remember is the suggestion that Jews were kicked out of all Roman colonies in 49, not just Rome itself. The fact that it is a group of women there sometimes is taken to mean that there weren't 10 Jewish men in town to form a synagogue.
The "we" passages end here and will later pick back up here. So we can presume that the author of Luke-Acts spent several years at Philippi. He would thus know the situation there, even if Acts itself does not make it clear.
It is a Jewish gathering, rather than a Christian one. Paul and Silas may talk to the women but it doesn't say there weren't men there, and Paul didn't go there with the expectation that there wouldn't be men. So I doubt the "there aren't 10 men" suggestion works, a suggestion that comes from later rabbinic literature anyway. I personally think it was the Christian Jews who were kicked out of Rome so Paul would have no reason to think that a generic synagogue would be outside the city because of the expulsion under Claudius.
The answer could be as simple as someone in Paul's group having heard there was a place of prayer by the river outside of Philippi. On the other hand, maybe it was common in the Diaspora for a synagogue or place of prayer to be located by rivers near cities. The water could have provided a means for ritual purification. Or did Christian Jews meet near rivers so that they could baptize?
We should keep in mind that a synagogue at this time was not a building, but a meeting. Most cities at this time probably did not have a synagogue building. Lydia was a non-Jewish merchant. Could it be that cities also often had synagogues for travelers near rivers so that strangers knew where to find them when they were passing through? So many questions we don't really have answers to.
5. Lydia is presumably married. Her whole household gets baptized, as does the whole family of the Philippian jailer later in the chapter. My hunch is that this included everyone in the family, including the children. This was a group culture, where the whole family followed the lead of the father. Our emphasis on believer's baptism strikes me as a modern individualist concern which, no surprise, rises with the rise of Protestant individualism.
This is a striking woman. She probably has a husband but, man, he is nowhere to be seen in this story. She invites them to her house. Her family follows her lead in baptism. Of course the rich never have to follow the norms of the rest of society, and she is probably a wealthy woman with a large house. A dealer in the dye of royalty! Luke's mention of her fits his emphasis on women as full participants in the gospel.
Apparently she and Luke didn't get the memo from Mark Driscoll and John Piper.
6. Philippian jailer... don't want too long of a post so I'll either leave this story for the book or come back to it later here.