Conclusion: The Song Is Not Ironic
Alright, so let's go over a couple of things...
Firstly, I do understand that this was a song and not an essay and that for artistic reasons she may have been unable to provide exposition prose regarding these examples. However, this does not invalidate the argument. Really, this examination of the song is intended to serve the identification of the issue that irony causes most people — that it is hard to apply and understand.
Secondly, this was not intended to be a definitive exploration of the song, just a quick look to address the examples. Many people when they have done this (often as a stand-up comedy routine) have attempted to twist the examples further so as to actually make the example ironic. However, they invariably come up with something that is still not ironic. Usually funny, but not ironic. We haven't even tried to do that because it's so difficult.