Original User: cdarti
For 1:
You can use the Attributes Tools>Generate From/To Node for Lines and then Find Next Downstream Line in Arc Hydro to determine the ids of the next downstream line. Your input line may be a shapefile for these 2 tools but must contain the field HydroID (long integer) storing IDs that uniquely identify your source line features. The HydroIDs will be used to populate the NextDownID field storing the HydroID of the next downtream lines. The most downstream lines will have NextDownID=-1.
If one line has more than one downstream lines, then the HydroIDs/NextDownIDs will be stored in an additional table called "sourceline"_FS, where FS stands for flow split and "sourceline" is the name of your input feature class. This table has 2 fields (FEATUREID=line HydroID, NEXTDOWNID).
For 2:
The network generated by Arc Hydro requires a polygon feature class as it establishes some additional relationship between the traditional geometric network that can contain only line and points and the area represented by polygons. In you case since you are interested only in points and lines you can use the traditional geometric network that can be created in the Catalog window or the geoprocessing tool. You stream features will become traceable edges in the network (just make sure you also set the flow direction in the network).
Christine Dartiguenave
Esri Water Resources Team