Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Viewport Visibility
ID_BASEOBJECT_VISIBILITY_EDITORParameter: Renderer Visibility
ID_BASEOBJECT_VISIBILITY_RENDERParameter: Enabled
ID_BASEOBJECT_GENERATOR_FLAGParameter: Display Color
ID_BASEOBJECT_USECOLORParameter: Color
ID_BASEOBJECT_COLORParameter: X-Ray
ID_BASEOBJECT_XRAYParameter: Position
ID_BASEOBJECT_REL_POSITIONParameter: Rotation
ID_BASEOBJECT_REL_ROTATIONParameter: Scale
ID_BASEOBJECT_REL_SCALEParameter: Rotation Order
ID_BASEOBJECT_ROTATION_ORDERParameter: Quaternion Rotation
ID_BASEOBJECT_QUATERNION_ROTATION_INTERPOLATIONParameter: Freeze All
ID_BASEOBJECT_FREEZEParameter: Unfreeze All
ID_BASEOBJECT_FROZEN_RESETParameter: Frozen Position
ID_BASEOBJECT_FROZEN_POSITIONParameter: Freeze P
ID_BASEOBJECT_FREEZE_PParameter: Frozen Rotation
ID_BASEOBJECT_FROZEN_ROTATIONParameter: Freeze R
ID_BASEOBJECT_FREEZE_RParameter: Frozen Scale
ID_BASEOBJECT_FROZEN_SCALEParameter: Freeze S
ID_BASEOBJECT_FREEZE_SParameter: Deform Position
ID_BASEOBJECT_DEFORM_POSITIONParameter: Deform Rotation
ID_BASEOBJECT_DEFORM_ROTATIONParameter: Deform Scale
ID_BASEOBJECT_DEFORM_SCALEParameter: Global Position
ID_BASEOBJECT_GLOBAL_POSITIONParameter: Global Rotation
ID_BASEOBJECT_GLOBAL_ROTATIONParameter: Transformed Position
ID_BASEOBJECT_ABS_POSITIONParameter: Transformed Scale
ID_BASEOBJECT_ABS_SCALEParameter: Transformed Rotation
ID_BASEOBJECT_ABS_ROTATION