Simutrans has much that isn't object oriented, but I wouldn't say that singletons are part of the reason.
1) simworld.c/h contains karte_t is what defines the map itself (karte means map) and a few more things. It's the most central class of all. This class is also at the boundary between the procedural part of Simutrans and the object oriented part.
2) All dialogs should be in the gui directory. I believe simwin.c/h is the starting point.
3) I don't think there are any specific files dealing with just the time. I would expect that the value is in karte_t somewhere. Drawing it on screen is probably done together with the rest of the status bar, which might not be a class at all. (If it is a class, it is not done in an object oriented fashion with regards to the time.)