No: the original source of the MP3 file was very likely a 16 bits one (such as a CD), so converting to a 16 bits FLAC with the same sample rate will retain all the original information. Even if the source had a larger bit depth (e.g. 24 bits), the effective bit depth of a mp3 stream (i.e. with a S/N ratio above 1) is far less than 16 bits anyway, so a 16 bits FLAC always do... That said, if your editing software can read the MP3 format, there's no need to convert the input file to FLAC at this point.
"changing the container ie mp3 to flac without encoding" is not possible. A FLAC file can contain only a flac stream (and creating a flac stream is already (lossless) "encoding")
Better: no; different: possibly.
[input file]-->Editing-->[intermediate file]-->Editing-->[intermediate file]-->Editing-->[output file]
Input file: as I wrote, if your input file in a MP3 one, and if your editing sofware can read MP3 files, there's no need to convert the file to something else. What is important is the chosen bit depth for the importation in the editing sofware.
Editing: since any editing step can potentially introduce noise because of the numerical round-offs, it is important to choose a bit depth larger than 16 bits: it can be 24 bits integers, or 32 bits floats.
Intermediate files: for the very same reason a lossless (compressed or uncompressed) format with 24 or 32 bits should be chosen. Since Audacity can read/write a wide range of file formats, FLAC is a valid option. Another option is the WAV format, embedding a PCM stream. A pcm stream just consists in the uncompressed audio samples. When creating it you have to specify the sample format (16 or 24 bits integer, or 32 bits float). In ffmpeg for instance this is:
-c:a pcm_s24le (signed 24 bits integer, little endian). FLAC can not handle 32 bits floats (but 24 bits is more than enough in practice).
- Advantage of FLAC: ~50% disk space saving on average
- Advantage of WAV/pcm: faster read/write
Output file: same criteria than for the intermediate files, as you don't know if you will edit it again or not in the future.