If I select a component and right-click->interface faces with model, the resulting edges are NOT inside the component. Is there any way to move the new edges into the component (or a group)?
I tried intersecting, copying, opening the component, and pasting, but I’m not getting them exactly where they need to be, since the new faces aren’t closed.

I suppose I could explode it, intersect, then recreate the component, but that’s a little unappealing.

Select the edges, hit Ctrl+X to cut them to the clipboard, open the component for editing and hit Edit>Paste in place.

Generally when I use Intersect Faces, I put the geometry to intersect inside the component using the method above before running Intersect Faces. This is especially useful when you need faces where the intersection occurs.

You can also open the component for editing, select the relevant faces and choose Intersect Faces with Model and the edges will be created in the correct context.

It’s worth noting that if you intersect the faces inside a group or component with geometry outside in order to cut the part, you won’t end up with faces at the intersection and you’ll have to deal with that. If the cutting faces are in the same context as the geometry being cut, you will leave faces as I show in my GIF, above. It’s not so bad to fix it if the cut is flat but when it’s more complex, it can be rather tedious.

When I need to do things like this I prefer to draw the cutting geometry outside of the component so I don’t risk modifying the component until I’m ready to do so. That also makes it easier to cut multiple components such as the tops of the back slats on Adirondack chairs or creating the pommel transition on the handlebar of this toddler’s trike.