Right, because you’ve been here since 2006 and have racked up over 8,000 posts I’m not gonna go easy on you either.
I don’t see why butterflys are relevant here, because you are not trading fungible instruments – you can’t replace a December future with a March future, or a 99 strike with a 101 strike. Not fungible.
Futures Fly – involves trading futures on the same underlying with different expiries, in the ratio +1:-2:+1. In this trade, you are speculating that, for whatever reason, the middle contract will over/under perform against the other two – for example, someone has bought the sh!t out of December ’14, and because of the volume/liquidity imbalance it’s got out of line with September 13 and March 14. Or, say, you are speculating when monetary policy changes will happen, and commentary from a member of the FOMC changes your opinion.
Options fly – involves options on the same underlying, with the same expiry, but with different strikes, again in the ratio +1:-2:+1. Here, you are speculating that the price of hedging the options will be less/more than the market expects, for example by underestimating volatility. I’ll leave that alone, there is another thread where this is mentioned (or search for Howard Cohodas’ thread where people far smarter than me explain it fully).
Now, moving on to the examples you give (lol)...
JESUS CHRIST!!
Yes, you can, and you are making the relative value trade that one will outperform the other.
So you are selling Gold, receiving USD, and exchanging them for AUD. In this case, you are speculating that the AUD against the USD will appreciate faster than the Gold does. Why you might want to do this I will leave aside.
Here you are doing the following: Buying EUR, Selling USD, Selling GBP, Buying USD. Assuming you do the trades at the same time and in the same amounts, your net position is then Long EUR, Short GBP, and you have no USD exposure. You have just legged in to a long EUR/GBP trade. If you don’t understand any of what I have said, after 6 years and 8k+ posts, I’d just give up. In face you should probably give up anyway, because it’s elementary stuff and you should understand it intuitively.