Tasker is probably the solution for automation on the Android platform. It...
How do I create a ".tar.gz" file using 7-Zip on Windows?
On Linux, I would simply run:
tar cfz archive.tar.gz folder
When using 7-Zip on Windows, this process is a little bit more complicated.
As a GZIP compressed archive can contain only one file, 7-Zip won't offer you GZIP compression if you try to compress a folder or multiple files at once. When you choose TAR, you can't select any compression algorithm.
The result is an archive with the .tar.gz extension which is exactly what you wanted to do.
That's another example how something that needs several mouse clicks on Windows needs a single line on a Linux shell.