Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Objects
CONNECTOBJECT_LINK
Parameter: Weld
CONNECTOBJECT_WELD
Parameter: Tolerance
CONNECTOBJECT_TOLERANCE
Parameter: Phong Mode
CONNECTOBJECT_PHONG_MODE
Parameter: Textures
CONNECTOBJECT_TEXTURES
Parameter: Center Axis
CONNECTOBJECT_CENTERAXIS