No. No open office. They will always use Microsoft Office, no questions asked. You can install Microsoft Office onto any OS. Nowhere in the rules does it mention anything but Microsoft Office.
Anything runs faster than IE, but the Web browser doesn't matter that much, although you should learn the basics: where the URL bar is, how to work the tabs, etc.
So, familiarize yourself with: IE, Mozila, Firefox, Chrome (<--- All very similar), Microsoft Office 2000, 2001, 2007 (<--- All kinda similar).
Just to make sure, I can submit a rules clarification, if anyone thinks that will work.
"Let's put all our differences behind us, for science. You monster."
Ubuntu is awesome.