There are several examples of how to do the former, see the Browser demo, Chat demo (from Chen's incubator directory) & makeover demo.
Login depends on the method you are using to login, e.g. basic authentication just requires a user header with the appropriate values. You can add a header using NetworkManager.addDefaultHeader()
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There is indeed a lack of XML parsing tutorials but generally this should be relatively easy.
XMLParser p = new XMLParser();
Element e = p.parse();
Vector children = e.getChildren();
Hashtable attributes = e.getAttributes();
To store XML I would just store the XML String itself since LWUIT doesn't provide the facility to save parsed XML data.
Storage.getInstance().writeObject("NameOfObject", xmlString);
String xmlString = Storage.getInstance().readObject("NameOfObject");