I have a particular question about transferring at Amsterdam Schiphol Airport. We had purchased Delta tickets to go to Edinburgh from the U.S., arriving on the August 30. Just found out the newly issued student Visa is not valid till August 31. So can't enter UK till that day. Instead of changing my original ticket, I am thinking buying a Eayjet flight from AMS to Edinburgh. Just wait at AMS for a long layover. Question is does the U.S.Delta flight passenger need to go through Passport Control at AMS to board Easyjet flight? Are arriving US flights and UK bound Easyjet on the same non Schengen side? So passenger doesn't need to go through Passport control?
As a US passport holder, passport check is a non-issue. You can enter the Schengen area for up to 90 days without visa if needed. But you could also go directly from your US flight to the non-Schengen part of the low-cost pier at Schiphol airport without entering the Schengen area (see the discussion following At Schiphol is 55 minutes enough for a transfer to an EasyJet flight?).
The main problem are the usual difficulties with “hidden city” ticketing. If you booked a return flight (outgoing journey and return to the US as part of the same reservation), you will lose the return portion of your ticket if you fail to show up for the Amsterdam-Edinburgh leg (of course if you booked two separate one-way tickets, this is not a problem).
And if you need more luggage than the carry-on allowance, you might have trouble convincing the airline to check it only to Amsterdam and not all the way to Edinburgh. If you do manage that, you would need to leave the arrival lounge/transfer area and go through the passport check to pick up your luggage and recheck it with Easyjet, but as I wrote above, this isn't really a problem, provided you schedule a lot of time for all the formalities.