Sometimes all you need is somebody pointing you to the stuff you were already looking for. So I wanna pass this on, and hope to help somebody else. Hopefully now you can google for "Debian XSD XML schema parser" and find this quick note:

Debian has a package called "libxml2-utils" that includes xmllint [1] which can already parse XML-schemas for some time now. As the whole world seems to use DTD, I nearly gave up on finding this tool. But here it is! Now you can parse your XSD-file with

xmllint --schema whatever.xsd

to parse the xsd document first (ignore the commandline help that shows up, too), and then you can check your XML-file with

xmllint --schema whatever.xsd myxmldoc.xml

Errors should show up at the end of the printed document.