I installed DSL on the mentionned machine. It works ; but I can hardly read the screen: darkblue characters ,on a black bord. Can this be altered?
You should have an image as your background (as in the screenshots that can be seen at www.damnsmalllinux.org), try right clicking on the desktop, a grey menu should appear, select "DFM for X11>Desktop Options" and try changing the colours with the settings in that window.
If the colours are out in program windows too, it might be a graphics driver problem, did they look alright when you booted the Live CD?
I also mannaged to download the audacityprogram, Think I have to unzip it (whit WinRAR?).
What type of installation did you do? HDD or Frugal?
If you got it from the MyDSL respository, it should have a ".tar.gz" or ".dsl" extension. The file named "audacity.uci" is the latest version available there, but you will need to make sure the PC loads it as part of the startup process (it doesn't stay there after shutdown). If you made a HDD install, the "tar.gz" package will stay on the computer after you install it (on a frugal install, it will need to be treated like a ".uci").
To transfer it to the old computer via usb-stick will be the easiest way, I guess?
Yep, just double click on the file (no need to "unzip" it) in the file manager (emelfm) and a line of text will appear in the box at the bottom saying it was installed (this won't be permanent unless you used the "tar.gz" on a HDD install). There should now be an icon on the desktop for it, and in the "MyDSL" folder in the DSL menu.
The Wiki pages on MyDSL extensions and persistance (if you're using a frugal install) should give you more info about using MyDSL.