Which free tools are available to work with AMR file format?
I need to open an
.amr file with this tool, play it and have the ability to to save part of it into MP3.
Audacity 1.3 beta supports amr files if you install the optional FFmpeg library. It should be able to do all the things you ask for.
The amr support was added in the Audacity 1.3.8 release. You can find info about that about half way down the bottom of the page.