But pigz shows that the unix pipeline philosophy works just fine. (of course compressing before tarring is probably better than compressing the tarred file, but that should be pipelinable as well)
Compressing first can also be slower if the average file size is smaller than the block size, because the main thread cannot queue new jobs as fast as cores complete them (this happens e.g. with 7zip at fast compression settings with solid archive turned off). Tarring then compressing means small files can be aggregated into a single block, giving both good speed and compression ratio.
Not if the files are similar. If you're compressing the files separately you'll start with a clean state rather than reusing previous fragments. Compressing a BMP after a TXT may not be beneficial, but compressing 3 tar'ed TXTs is definitely better than doing them separately.
AFAIK the gzip command still cannot compress directory information and therefore needs tar in front of it if you want to retain a folder structure.
TIL: you can use method 93 - Zstandard (zstd) Compression - with ZIPs