Also, of course, prices may be slightly differ depending on people who are trading there. The persons who usually equalise the prices are called arbitragers. They see the price difference, and quickly buy on one market and sell on another. When there are many people doing this, the two prices equalise. This happens on non-crypto markets too.
That they don't have fiat isn't the reason for the difference i think. Bittrex offers trading in USDT aswell ( USD$ in Tether.)
Has more to do with actual volume, and just the supply x/ demand and, as a result arbitrage.
Yeah, maybe you're right, but volume and demand themselves depend on the ability to 'import' fiat, I can suppose.