I travelled between Sydney and Los Angeles via Virgin Australia in 2011, and they had no Wi-Fi then.
On the other hand, I had Wi-Fi on a flight between New York and San Francisco on American Airlines.
I don't think so, usually the wifi is supported by a land base carrier, and of course they don't have that on the ocean yet. So no they most likely don't. You should look it up to see if your airline has it.
You can check on the website with your flight numbers and the features of the airplane.
It should have something like extra leg room, meal, movie, wifi, ect...
I travelled between Sydney and Los Angeles via Virgin Australia in 2011, and they had no Wi-Fi then.
On the other hand, I had Wi-Fi on a flight between New York and San Francisco on American Airlines.
I hope you're not being serious. I hope this is a joke and you understand the huge difference between those flights.