Compress files while reading data from STDIN

Yes, gzip will let you do this. If you simply run gzip > foo.gz, it will compress STDIN to the file foo.gz. You can also pipe data into it, like some_command | gzip > foo.gz.

Yes, use gzip for this. The best way is to read data as input and redirect the compressed to output file i.e.

cat test.csv | gzip > test.csv.gz

cat test.csv will send the data as stdout and using pipe-sign gzip will read that data as stdin. Make sure to redirect the gzip output to some file as compressed data will not be written to the terminal.

gzip > stdin.gz perhaps? Otherwise, you need to flesh out your question.