can't answer all your questions with 100% certainty but i'll try though
q1: Yep - the network is called UniWireless, just configure your wireless settings and you're good to go. Instructions on how to do that can be found
here.
q2: By 'surrounding campuses' do you mean the nearby non-Melbourne Uni ones such as RMIT? If yes, there's this thing called Eduroam, where partner institutions can share the wireless facilities (to a certain degree). Like if you visit another uni, you can instantly access the internet. I don't know which are the participating institutions though, although I'm sure Melbourne Uni is one. More info can be found
here. Configuration is most probably different from that of the UniWireless.
q3: It's relatively fast - that's why some students download their music on campus. According to the IT FAQs, it's up to 54mbps. Be warned that there's a download limit for external traffic of 250Mb per week, once you exceed this, you can only access internal websites (like LMS, Portal, etc.) Also, since it's a shared facility, the speed would usually be lower than 54Mbps for most users.
q4: I have no idea since I've never used xboz 360 live before. But if people's opinions in Yahoo Answers are anything to go by, then yes, the speed is more than adequate for it.
Cheers.