The programmatic way of getting the superclass of a given class is documented at http://demo.qooxdoo.org/current/apiviewer/#qx.Class
<classname>.superclass
or getting the name of the superclass as a string
<classname>.superclass.classname
which means that e.g.
qx.ui.core.Widget.superclass.classname
will return the string "qx.ui.core.LayoutItem".
Regarding the programmatic way to retreive all subclasses of a class:
This is currently not possible without iterating the whole class hierarchy/tree and testing the objects against being subclasses of the given class.
We discussed at https://gitter.im/qooxdoo/qooxdoo that it maybe would be usefull to create an array for each class holding the subclasses. This could be added to the code of the private method __createClass in qx.Class.
We would like to encourage everyone who needs this (or other) functionalities to join us on https://github.com/qooxdoo/qooxdoo/ and help extending qooxdoo by creating a pull requests. Thank you.