Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Objects
CONNECTOBJECT_LINKParameter: Weld
CONNECTOBJECT_WELDParameter: Tolerance
CONNECTOBJECT_TOLERANCEParameter: Phong Mode
CONNECTOBJECT_PHONG_MODEParameter: Textures
CONNECTOBJECT_TEXTURESParameter: Center Axis
CONNECTOBJECT_CENTERAXIS