I see what you’re doing…
There is the Dashed Line plugin which is available from Smustard that would do what you need. You can make dashed lines manually by dividing an edge and hiding alternating segments. Here’s a quick example.
Without going into a long thing, since SketchUp is a surface modeler, lines are used as edges to define the limits of faces. They weren’t really intended to be used as lines per se. I won’t get into whether that should be changed or not although I expect someone will be along to do that. If you need to do this frequently, it might be best to invest in SU Pro and use LayOut. It’s got options for different line weights and styles including dashed lines.
The AA thing was a shot but it’s dependent on the setting you already have and your graphics card.