Hi Marina
I do this type of work all the time, design in sketchup and then have parts lasercut or CNC routered -I can give you a few pointers.
The first thing you need to know and understand is that sketchup does not create true arcs,circles elipses etc. All of these geometric entities are broken into segments. Sketchup is especially poor at exporting solid 3d models for this reason and there are very few instances where exporting a 3d is useful in other software packages especially where one intends using the model for any type of CNC cutting.
However I get very good results using one particular plugin for getting machines to cut stuff for me its called- Tak2hata: Create Section Drawing. Install it by searching for it with the sketchucation tools- a plugin you must install if you havent already
How it works is: a)you create a section through the part you want to cut b)right click on the section you have created c)create section drawing
This exports a 2D dxf of the section you want cut as well as skp model of the 2D section. It eliminates all kinds of problems you may experience getting goemetry or faces on the right planes and really solves a lot of headaches for me.
Note though: As I explained earlier- sketchup does not export true arcs or ellipses and you would therefore get very staggered unatractive arcs if you did this with the model you have uploaded. My solution is to increase the number of segments SU uses to describe an arc or elipse. This has to be done with the geometry BEFORE you extrude it.
Method as follows a) draw arc/ellipse b)right click on it and select [entity info] c)you are then allowed to increase the number of segments in the entity info dialog box. This will give you something which comes much closer to the geometry you really want cut.
Please note: after you have extruded an arc or ellipse you cannot edit the number of segments which describe it.
Hope this helps
Stephen