There is no way to import text and line tepe, color. But...
We can import dwg to LayOut via SketchUp scene with style.
Then we can get vector and bitmap from imported SketchUp model, so you can change line type, color with LayOut way.

Set the imported SketchUp model (scene) to Hybrid or Vector. (Window menu - SketchUp model) Right crick imported SketchUp model and select 'explode' and 'ungroup'

You should be controlling layer visibility with scenes in SketchUp and using those scenes for viewports in LayOut. Then you don't need to control SketchUp's layer visibility in LayOut.

What do you have for render settings in LayOut? Very likely the edit render setting is set to less than High so imported images won't look very sharp. Export render quality can be set higher and the image will probably look good. Try importing your image and making a PDF export at high or even medium quality.