I think the wet suit is for prevention of jelly fish stings. We snorkled in Cairns and did not see any jelly fish but the outfitter insisted we wear wet suits.
I'm pretty sure you can't get on the plane without that, right? I think I had a friend scrambling to do his in the airport terminal, or maybe even had to go home?
To stay in Australia, yes. The visa is attached to your passport, and when the ticket counter runs your passport, the visa shows up.
However, you can transit through Australia without a visa under certain conditions when on your way to somewhere else. You cannot leave the terminal where you land in Australia (your connecting flight has to leave from the same terminal), you must have a valid visa for your final destination, and you cannot be in Australia more than 8 hours. Finally, the airport in Australia has to accept TWOV (transit without visa) passengers. We have personal experience with this from our trip last winter. We were heading to Auckland for a cruise that ended up in Sydney. His visa was delayed, and we had a layover in Sydney. We had to jump through all kinds of hoops, but we got him on the damn plane.