If I change ArcMap to edit unversioned data, how do I continue to edit data in ArcSDE that are versioned (due to being in a network, for instance)?
You will only have to make unversioned edits when setting up the generate id table.
1: For intersecting_edge, you must have a be using a geometric network on the feature that is being created/modified and the edge you wish to select. It will only copy one field from the intersecting feature into one field of the source feature. If you want to copy more multi fields from the intersected feature and you can look at intersecting statistics with the CONCAT option, then use a Expression rule to break them into multi fields
http://resources.arcgis.com/en/help/localgovernment/10.1/index.html#/Intersecting_statistics/028s000...
2: You can edit unversioned data, you just need to change the editor options in ArcMap to do this.
3: I do not understand the question, can you provide more details? If a field has a relationship tied to it, changing the value with affect the relationship to related records
If you are just trying to copy the value from you ID field and place that in feature that is intersecting it, you willl have no problem.