Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Mirror Plane
SYMMETRYOBJECT_PLANEParameter: Weld Points
SYMMETRYOBJECT_WELDParameter: Weld Tolerance
SYMMETRYOBJECT_TOLERANCEParameter: Symmetrical
SYMMETRYOBJECT_ONPLANEParameter: Clamp Points on Axis
SYMMETRYOBJECT_CLAMPPOINTSParameter: Delete Polygons on Axis
SYMMETRYOBJECT_DELETEPOLYGONSParameter: Automatically Flip
SYMMETRYOBJECT_AUTOFLIPParameter: Flip
SYMMETRYOBJECT_FLIPParameter: Convert to New Symmetry Generator
SYMMETRYOBJECT_CONVERT_LEGACY