Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Use Shading Mode
DISPLAYTAG_AFFECT_DISPLAYMODEParameter: Shading Mode
DISPLAYTAG_SDISPLAYMODEParameter: Style
DISPLAYTAG_WDISPLAYMODEParameter: Volume Vector
DISPLAYTAG_VDISPLAYMODEParameter: Use Level of Detail
DISPLAYTAG_AFFECT_LEVELOFDETAILParameter: Level of Detail
DISPLAYTAG_LEVELOFDETAILParameter: Use Visiblity
DISPLAYTAG_AFFECT_VISIBILITYParameter: Visibility
DISPLAYTAG_VISIBILITYParameter: Use Backface Culling
DISPLAYTAG_AFFECT_BACKFACECULLINGParameter: Backface Culling
DISPLAYTAG_BACKFACECULLINGParameter: Use Materials
DISPLAYTAG_AFFECT_TEXTURESParameter: Materials
DISPLAYTAG_TEXTURESParameter: Use Reflections
DISPLAYTAG_AFFECT_REFLECTIONSParameter: Reflections
DISPLAYTAG_REFLECTIONSParameter: Use Tessellation
DISPLAYTAG_AFFECT_TESSELLATIONParameter: Tessellation
DISPLAYTAG_TESSELLATIONParameter: Enable
ONION_USEParameter: Draw Mode
ONION_MODEParameter: Scale
ONION_SCALEParameter: Size
ONION_PSIZEParameter: Shading Mode
ONION_DISPLAYMODEParameter: XRay
ONION_XRAYParameter: Frames Before
ONION_FRAMES_BEFOREParameter: Frames Before Color
ONION_COL_FRAMES_BEFOREParameter: Frames After
ONION_FRAMES_AFTERParameter: Frames After Color
ONION_COL_FRAMES_AFTERParameter: Frames Step
ONION_FRAMES_STEPParameter: Use Range
ONION_ONLY_RANGEParameter: Start
ONION_FROMParameter: End
ONION_TOParameter: Use Keys
ONION_USE_KEYSParameter: Keys Before
ONION_KEYS_BEFOREParameter: Keys Before Color
ONION_COL_KEYS_BEFOREParameter: Keys After
ONION_KEYS_AFTERParameter: Keys After Color
ONION_COL_KEYS_AFTERParameter: Use Custom
ONION_USE_CUSTOMParameter: Custom Frames
ONION_CUSTOMParameter: Custom Color
ONION_COL_CUSTOMParameter: Use Cache
ONION_CACHEParameter: Calculate Cache
ONION_CALCULATEParameter: Empty Cache
ONION_DELCACHE