Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See page_maxonapi_getting_started_foundations_cinema_parameters.
Parameter: Use Shading Mode
DISPLAYTAG_AFFECT_DISPLAYMODE
Parameter: Shading Mode
DISPLAYTAG_SDISPLAYMODE
Parameter: Style
DISPLAYTAG_WDISPLAYMODE
Parameter: Volume Vector
DISPLAYTAG_VDISPLAYMODE
Parameter: Use Level of Detail
DISPLAYTAG_AFFECT_LEVELOFDETAIL
Parameter: Level of Detail
DISPLAYTAG_LEVELOFDETAIL
Parameter: Use Visiblity
DISPLAYTAG_AFFECT_VISIBILITY
Parameter: Visibility
DISPLAYTAG_VISIBILITY
Parameter: Use Backface Culling
DISPLAYTAG_AFFECT_BACKFACECULLING
Parameter: Backface Culling
DISPLAYTAG_BACKFACECULLING
Parameter: Use Materials
DISPLAYTAG_AFFECT_TEXTURES
Parameter: Materials
DISPLAYTAG_TEXTURES
Parameter: Use Reflections
DISPLAYTAG_AFFECT_REFLECTIONS
Parameter: Reflections
DISPLAYTAG_REFLECTIONS
Parameter: Use Tessellation
DISPLAYTAG_AFFECT_TESSELLATION
Parameter: Tessellation
DISPLAYTAG_TESSELLATION
Parameter: Enable
ONION_USE
Parameter: Draw Mode
ONION_MODE
Parameter: Scale
ONION_SCALE
Parameter: Size
ONION_PSIZE
Parameter: Shading Mode
ONION_DISPLAYMODE
Parameter: XRay
ONION_XRAY
Parameter: Frames Before
ONION_FRAMES_BEFORE
Parameter: Frames Before Color
ONION_COL_FRAMES_BEFORE
Parameter: Frames After
ONION_FRAMES_AFTER
Parameter: Frames After Color
ONION_COL_FRAMES_AFTER
Parameter: Frames Step
ONION_FRAMES_STEP
Parameter: Use Range
ONION_ONLY_RANGE
Parameter: Start
ONION_FROM
Parameter: End
ONION_TO
Parameter: Use Keys
ONION_USE_KEYS
Parameter: Keys Before
ONION_KEYS_BEFORE
Parameter: Keys Before Color
ONION_COL_KEYS_BEFORE
Parameter: Keys After
ONION_KEYS_AFTER
Parameter: Keys After Color
ONION_COL_KEYS_AFTER
Parameter: Use Custom
ONION_USE_CUSTOM
Parameter: Custom Frames
ONION_CUSTOM
Parameter: Custom Color
ONION_COL_CUSTOM
Parameter: Use Cache
ONION_CACHE
Parameter: Calculate Cache
ONION_CALCULATE
Parameter: Empty Cache
ONION_DELCACHE