1) That is a Vandals song which No Doubt covered, as an homage and a message. You should pick up that album, it's fantastic and hilarious. Way lewd though, not for listening to around the kiddies.
2) It's okay if you didnt know whose song it actually is lol I aim to inform, not criticize :) Punk and its lore are often obscure.
It's also okay if you didnt know (to the first responder on this thread) that there are several different kinds of skinheads in punk rock. Most actually are very vocally ANTI racism, but there are some bad eggs out there too for sure. They're usually really easy to tell apart if you know what to look for.
As for Oi music, the violence is less a part of this subculture than it used to be, but it's really dependent on the individual band. The main themes tend to be brotherhood and family, unions, strength of the working man type stuff.
3) There's a bunch of punk history about why we say Oi Oi!, but it boils down to some of our favorite bands started it (Cockney Rejects, Ramones, amongst others) and there's often a callback/response at punk shows which is so rad and so much fun.
4) All of the other person's answers sum up the rest.
5) "Oi to the world and everybody wins" is talking about another huge theme in 3rd wave+ (so late 80s into 90s, onward) punk rock, which is Unity. The real punks (except for the piece of crap GG Allin set, essentially the Nihilists) believe in helping each other, in service, in peace and unity amongst humankind. It's an inclusive statement meaning we can all be brought together because we are all different and yet all the same.