How does ffmpeg record -timecode in different file formats? As a followup to Add timecode information to file
ffmpeg documents the -timecode parameter:

-timecode hh:mm:ssSEPff
Specify Timecode for writing. SEP is ’:’ for non drop timecode and ’;’ (or ’.’) for drop.

Two questions come up:

Which container formats support the -timecode option? Are there any that don't?

The option to specify DF/NDF timecode implies the ability to store DF flag in the file alongside the framerate. Is that how it works, or does ffmpeg convert DF timecode to a corresponding NDF frame count and stores that?
FFmpeg only supports timecode in a limited set of formats. They are the MOV family (MOV/MP4/3GP..), MXF family, raw DV and Grass Valley GXF.
How the timecode is stored and flagged is specific to the format. MOV stores a DF flag, integer framerate and the timecode as a rate-adjusted integer frame index. MXF does essentially the same.