Convert zip to gzip and upload to S3 bucket
Looks okay to me in general.  I'd prefer to pass in configuration
separately, parsed from a config file or command line arguments, but if
it's a one-off script it's probably okay this way.

The temporary files aren't deleted as far as I see; consider using the
tempfile module to
allocate and delete temporary files automatically.

Also, while the string to bytes conversion works as is, it's also
brittle when used with large files, e.g. larger then the amount of RAM
available, because it will store the downloaded file in memory.  I'd
suggest passing in gz.write directly instead:

with gzip.open(tmp_dir + tmp_fname, 'wb') as gz:
    ftp.retrbinary('RETR ' + fname, gz.write)


Unless I'm mistaken that should keep the bytes in order; if not you
could still pass in a function that converts only the downloaded chunk
to bytes and calls gz.write on the converted value.

Regarding your questions:


Since there's no extraction of data from the zip file, I don't see how
that matters.  If you were to extract something (a single file) from
the zip file, then yes, gzipping that will of course be okay.  Make
sure that the gzipped files are how you expect them (i.e. a single
compressed text file) and that you don't need the file name or other
attributes in the original zip archive.  At the moment you basically
upload some_file.zip.gz to S3, as in, two compressions nested.
Probably not what you want.
As argued above that's probably not advisable unless you know that the
data fits into memory.  If it does, sure, why not.


Some more remarks:


The zipfile import is unused, as mentioned above.
Prefer
os.path.join
to concatenating strings.
fname/passwd instead of filename/password seems pointless
truncation.
print should be used as a function to be forwards compatible,
i.e. print(e) instead.
The result of tmp_dir + tmp_fname should be reused instead of
writing the same expression twice.