Not necessarily.
I've written about this a few times before on the forums. There's also a blog explaining things in more detail, you can read that
here.
It's important to remember that Luno's price is solely determined by supply and demand, as any other market is. Different countries will see different rates. I remember an exchange in Zim that was trading at ~$2000 premium at one point. In no way is there any correlation in supply and demand, and market conditions are extremely different between Kraken and Luno.
Sure, if everyone arbitraged the price will most likely correct to what's listed on most USD BTC pairs internationally. The fact that arbitrage trading isn't available to everyone and generally sees high/ limited fees and funds leaving SA is a part factor here.
I'm not sure why we'd want to trade our customers funds? We've gained our reputation by being a trusted exchange and brand in the Bitcoin space, why we'd want to wreck that by doing something like this makes absolutely zero business sense. Remember that everything is also publicly available on the Blockchain, you're welcome to dig around

Either way that's quite a wild assumption to make. Do you have any data or insights to backup your argument and theory?
My response above should cover most of your question too

The price difference will fluctuate.
I'll bookmark this post and link to further questions about the price differences.