I can't say I'm a fan of that approach. The drop-down means I have to navigate up to the toolbar and then click twice to change the selection mode, rather than the conventional way of just dragging the other way. This would be high up on my list of feature requests.
The problem is not with printing. The problem is with opening the DWG file. I assume that the DWG file uses color for line thickness. When you open the DWG file you can customize how the file is opened in SE 2D Drafting. Click on the Options button at the bottom of the File Open dialog. This will take you to the AutoCAD to Solid Edge Translation Wizard. On one of the pages of the wizard you will be able to define the Solid Edge Line Widths relative to the original AutoCAD colors.
I could not find "Options". I opened Solid Edge 2D Drafting ST4. Then clicked on Solid Edge Viewer. The screen opened. I opened a dwg file (No ptions shown) I clicked on Open and drawing appeared on the screen (Again No Options shown) I printed the drawing and again got very light lines. Where Is the "Option" option?