1: The listing would need to move in proportion to the currency movement. It's not that it wouldn't move, it's a question of proportionality. If the USD is the world's safe haven (and it is) then money will (and does) always run to the USD in times of crisis. Even during the GFC, which was caused by the U.S banking system, several trillion dollars of capital moved INTO the NYSE and USD because other countries were actually more effected by the subprime crisis than america was. As the saying goes, if america sneezes, the world catches a cold. So you can imagine that if the USD is the safe haven currency, investors might be willing to sacrifice a bit of their book value to have their asset held in USD rather than AUD or GBP or whatever. To put it another way, the asset might end up being worth more in USD precisely BECAUSE it's the safe haven currency. In other words, investors will overpay in order to just get their capital denominated in USD/get on the safe side of currency risk. Again, this depends on the asset, but the thing to remember is that you're working with a preference to have your holdings both in a particular asset and in a particular currency - you've introduced a 2nd variable and that variable may have different figures on either side of it. I hope that makes sense?
Here's an example I did with gold a little while ago:
Here we go:
View attachment 107099
GOLD australia (an etf that sells tenths of an ounce) vs GLD united states (which is also an etf that sells in tenths).
Exchange rate difference in the past 3 months:
View attachment 107100
AUD's pulled 13% against the USD but there's only a 10 percentage point difference in the price.
1/1.13=0.88
0.88*1.18=1.04
vs
1/1=1
1*1.09=1.09
Significantly better off holding it in AUD
In the case of gold, the perth mint's etf is dual listed but even with exchange rate factored in is worth more on its ASX listing than its NYSE listing.
2: Yep absolutely. If the AUD tanked by, say, 10%, then your holding would bounce by something close to 10%. If you want to add currency exposure and don't want to dick about with w-8 forms, international accounts, conversion fees, brokerage fees etc etc etc then it's a great way to do it.
Thing to remember though: Let's say the NYSE doesn't move but the AUD tanks. So the AUD listed NYSE ETF will obviously bounce in AUD as you now need more AUD's to buy one. But if you owned it denominated in USD, those USD's are now worth more in AUD's once you convert them. So you have to ask yourself which will be higher and/or if it's worth the headache of opening an international account, exchanging the money, coughing up the fees etc etc.
One big caveat: The liquidity/daily volume of the nyse listing will be literal orders of magnitude higher. Take a look at spy vs spy.ax for example:
Several hundred million daily trades vs a few thousand.
3: You've basically just gotta ask yourself whether you think investors would rather hold it in AUD or USD. Usually (and gold was an exception I showed above) it'll be USD. However, the other thing to think about is currency exchange fees, brokerage fees, and management fees of the etf's themselves, which can really add some sting to whatever you're doing, as well as the volume/liquidity problems you might have holding it in AUD as I showed above.