4.1 What parts of the Python library are supported?
The good news is that Jython now supports a large majority of the standard Python library. The bad news is that this has moved so rapidly, it's hard to keep the documentation up to date.
Built-in modules (e.g. those that are written in C for CPython) are a different story. These would have to be ported to Java, or implemented with a JNI bridge in order to be used by Jython. Some built-in modules have been ported to JPython, most notably cStringIO, cPickle, struct, and binascii. It is unlikely that JNI modules will be included in Jython proper though.
If you want to use a standard Python module, just try importing it. If that works, you're probably all set. You can also do a dir() on the modules to check the list of functions it implements.
If there is some standard Python module that you have a real need for that doesn't work with Jython yet, please send us mail.