No, your second sentence is not right either. It would be right with 'a' (grammatically).
No, your third sentence is not right. It would be better with 'a'. But what surrounds Australia are several seas, and in fact several oceans - Pacific, Southern, and Indian. I'm not sure about Hawaii. Sicily is surrounded by the Mediterranean Sea.
The usage of 'ocean' and 'sea' in not straightforward. There are only (about) seven named oceans, whereas there are hundreds of named seas. Sometimes, " the sea" and "the ocean" mean the same thing. But "a sea" is not "an ocean". To say that an island is surrounded by sea/ocean (zero article) is OK. If it is surrounded by a sea/an ocean/ the sea/the ocean, then that's what defines it as an island - so this sentence is necessarily true (for most usages of 'island'). But then, Australia is surrounded by the ocean/sea, and it's not called an island because it's designated as a continent. Therefore, Greenland is the largest island, while Australia is the smallest continent.
[Not a geographer]