We have the same problem, tested in 2012 and 2013. I have changed pretty much every parameter related to line thickness, layer and DWG export and it will not export correctly.
Does anybody know how to avoid the 0mm line thickness
At the risk of sounding like I'm making apologies - are you sure the problem is with SW? In looking at the png file, the dashed lines are clearly visible so the weight can't be .000. It also does not appear to be any different from the black lines in the ACAD dwg.
Ahmet, check your DWG mapping file to make sure that hidden lines are set to either a bylayer lineweight or check the option to only map entities already on layers.