Hello, the original post diverted to two topics, let me clarify them.
Starting with the sketch import, we support the two most common sketch formats in the CAD industry: DXF, and DWG. There are a lot of formats that we could also support, but I cannot tell you any exact details about them. Especially with Illustrator, we have seen many times that it tends to export glitchy DXF sketches. For some reason, sketch control points got tangled during the AI-DXF conversion.
There are some sketch elements that cannot be imported to the modeling space like hatches and text objects, but those trigger a different error message which tells those unsupported elements will be skipped.
STL format is a different story. Shapr3D is a CAD modeling tool while STL is a mesh file with a whole different structural background. If you wish to transfer your data without losing any significant details, please always use CAD file formats like X_T, STEP, or IGES.
edit: can you please tell me what are the features you are using Illustrator for sketching instead of the sketch tools of Shapr3D?