In Australia, if after an election no party can form a government, either by themselves or by coalition, another vote must be called. I understand that all the lower house seats are up for grabs, but what about the senate? If the senate seats are also included, in a double-dissolution election are all these seats included or only half?
Government is formed in the lower house (the House of Representatives), so an inability to form government resulting in a second election doesn't affect the terms of the senators. They're in no matter what, for the terms they were elected for.
So the situation with senate seats wouldn't differ between a standard election and a double dissolution election (as this upcoming 2016 federal election is).
If a single party or coalition can't claim a majority of seats (76, given there's 150 seats), then generally, as you stated, another election would have to be called.
However in practice this doesn't happen. Because the people hate going to a vote, there's considerable pressure for the elected representatives to find a solution to prevent both the expense and hassle (and therefore, potential electoral punishment) of another election.
This happened recently, in the 2010 federal election. Both major parties won 72 seats each, 4 short of a majority. At the time there was media speculation - as there always is - that a second election might result. But after a bit of wrangling, and a speech that was much longer than anyone needed, four other members agreed to support the Labor party (on at least budget supply and no-confidence motions), giving them the right to form government without requiring another election.
The previous time this happened federally, in 1940, a second election was also avoided. And, hung parliaments have occurred many times in state and territory elections as well. As far as I'm aware none of these have resulted in second elections.