I have an old version of Audacity with many files. If I download the latest version, will I lose my old files and songs? My current version is 2.0.4

Check that your files work with your current version of Audacity before you upgrade.
Audacity 2.2.2 supports projects created with older versions, so as long as they work with your current version, there should be no problem with upgrading.
Also, there is due to be a new version of Audacity in a few weeks. Again this is backward compatible, so there should be no problem updating again in a few weeks.

As a general rule it’s a good idea to export to WAV or FLAC (or other “regular” audio format). You’ll always be able to open/edit those with Audacity or any other audio editor, or you can play them with player-software, or make CDs, etc.

I recommend exporting to a regular audio format whether you make an AUP project or not.

And of course, if the files are important make back-ups!