Hi macmac,
Those are optional things to do in the game. Missing them out shouldn't cause a dead end, but it might not be possible to do them now that the train has blown up.
When I played Chapter 1, I didn't manage to find the purse, but all that transpired was that I received a scolding about it from another character in the next chapter.
I suppose that gives the game an extra edge of replayability.