Depends on your final destination. There are several airports that are international where you could land and you may transfer depending on your destination, the airline, and the time of day. To give you an exact answer we would need more information.
Eastbourne doesn't have an airport - the nearest is Gatwick, so you would have to fly from Edinburgh to Gatwick and take a train from Gatwick to Eastbourne.
You can't fly directly. It would have to be Sacramento to LA. LA to London. London to Edinburgh. Edinburgh to St Andrews by bus or train.
yes you can
Yes, you can get a one day 'tartan visa' (similar to the visa waiver program) when you land in Scotland.
The easiest and quickest way is to fly.
By aeroplane.Ryanair is the cheapest.
About 8 hours
You can't take a train directly from the Shetland Islands to London. You can't even fly directly between Shetland and London. You could travel by boat from Shetland to Aberdeen and then take a train or fly from there to London or you could fly from Shetland to Edinburgh and either fly or take a train from Edinburgh to London.
3 hrs
About 3 hours.
About one hour.
you would fly west towards the setting sun like going to Hawaii