I expect the dimension in your first screen shot is on a layer lower in the list than the viewport. I always keep dimension and other text layers above the layers I put viewports on.
As for the section plane, you may have turned it off in SketchUp but I'm guessing you didn't update the scene's style. Section plane visibility state is a style setting. You can turn it on or off without updating the style but then the state doesn't get transmitted to layout.
Section cut lines are not snappable edges. You can place a section cut face or create a group at the section cut to get edges and corners you can snap to. Sometimes I just use guidelines to create snap points. Then I delete them when finished.