EDIT: you could also read some code here, this is for generating epub, not reading them but the code may be useful.
EDIT again: And see links to related question in the right sidebar, there are some links in the answers to free ebook reader which support ePub.
EDIT 3: You should add a comment when you edit your question so people who answer you can continue the discussion (if you don't comment we're not noticed of your edit).
So, The parsing fail because you didn't read the spec or related questions on Stack Overflow... *.epub file are a zipped folder containing XML file(s), not plain xml.
I read through this tutorial once (free registration required, sorry) and it gave me a great introduction to ePub. deverloperWorks tutorial here
I highly suggest you look at some of the XML processing libraries. If you just want to get specific information out of the XML file, then you can pick the right parsing strategy.
3) unzip it to a subdirectory in your app's documents folder using the zip library, linked above
4) parse the XML file at META-INF/container.xml (if this file doesn't exist the EPUB is invalid) using TBXML, linked above
5) In this XML, find the first "rootfile" with media-type application/oebps-package+xml. This is the OPF file for the book.
6) parse the OPF file (also XML)
7) now you need to know what the first chapter of the book is.
a) each <item> in the <manifest> element has an id and an href. Store these in an NSDictionary where the key is the id and the object is the href.
b) Look at the first <itemref> in the <spine>. It has an idref attribute which corresponds to one of the ids in (a). Look up that id in the NSDictionary and you'll get an href.
c) this is the the file of the first chapter to show the user. Work out what the full path is (hint: it's wherever you unzipped the zip file to in (3) plus the base directory of the OPF file in (6))
8) create an NSURL using fileURLWithPath:, where the path is the full path from (7c). Load this request using the UIWebView you created in (1).
You'll need to implement forward / backward buttons or swipes or something so that users can move from one chapter to another. Use the <spine> to work out which file to show next - the <itemrefs> in the XML are in the order they should appear to the reader.
Jonathan Wight (schwa) has developed a ObjC solution for parsing and displaying ePub documents on the iPhone. It's part of his TouchCode open source repository.