using qgis, I have a polygon layer. It has only one feature in the attribue table. But it has lots of different areas, clearly separated from each other. Now I want to have this separate areas also in separate features, to be able to sort according to size etc. Trying different ways with the Geoprocessing tools did not help (singlepart to multipart, dissolve).
Singlepart to multipart wouldn't work as you've described a multipart geometry. Try 'Vector > Geometry Tools > Multipart to Singleparts'. This will create a layer with all individual polygons.
Next you can edit the attribute table to include an 'AREA' column using the field calculator with:
You can now sort by size.