US citizens living overseas are not double taxed. You get the 2555 exclusion for the first $80K or so in income, which the US won't tax at all. Above that you take the 1116 deduction which allows you to deduct the tax paid to the foreign country from what you would owe as a US citizen. Since the tax rates in most countries (including Great Britain) are higher than the US Federal tax rates, you don't end up paying much of anything to the US government. The main exception is if you live in a place where tax rates are lower than US Federal rates, there you'll end up paying some tax. But look what a great government you get for your money!
If you're paying double, get a good accountant, or figure it out for yourself.
As for what questions US Immigration can ask you, the answer is "anything they like". If you want to prove you've got more testosterone than the guy asking the questions, then argue with him. If you want to get where you're going, just tell him you're going to visit family. End of story.