If I buy an iphone via a shop who gets to book the vat, the shop or Apple? If its Apple why do they have a greater claim over someone else further up the chain?

If I buy an iphone as part of a Vat registered business I can claim that vat back. So does that Vat get booked twice?

It is paid by consumers because they are the ones that ultimately pay it. Businesses that pay vat can claim it back so that the 'value added' only gets taxed once. Apple has added value, but so have others.

If you know economics, then you should also know that while demand is proportional to the total asking price, it’s not a linear relationship. So whatever the price is paid, it’s mainly paid by customers.