As for the "special relationship"- how much does it really matter? From realpolitik perspective the UK's importance is limited to their veto capacity in the EU and UN(the latter which is shared by America) and US access to the UK's overseas island naval bases. Their's nothing their that they can't get from other countries. America's real special relationship is with Saudi Arabia.
No. The UK has been the US' most steadfast ally.
Saudi Arabia is just unreliable (70's oil crisis/hotbed of terrorism) and you are overstating its particular importance as a source of US oil. It varies but we only get around 10-20% of our imported crude from Saudi Arabia. We get 2x as much from Canada. Of course, a stable Saudi is good for America and the global economy so it helps to have good relations in place.
Have they? Firstly I don't see the relevance of steadfastness if it's not coupled with power... you might as well call Malta "your most steadfast ally". UK can't give you much more then a veto in the EU(which you could pretty easily from other European countries) and access to strategically valuable islands(all of which are far from irreplaceable.) And I doubt the UK has been a more steadfast then Canada, Australia or Israel... all three of which are far more valuable to America then then the UK is, from a realpolitik perspective(and in the case of Canada and Israel, probably from a sentimental perspective as well).
As for Saudi Arabia, all that oil counts a lot more then a few shady citizens. The thing about oil is that the source your oil comes from isn't relevant- oil prices are more or less bound at the hip on an international scale, so even if 0% of your oil came from SA they would still have just as much of an impact on your prices. More importantly Saudi Arabia is America's only reliable base for attacking Iran(as it was previously for attacking Iraq): Israel is too distant and staging an attack from Israel would be a PR disaster, Kuwait/UAE/Bahrain are too vulnerable to being knocked out before America's army gets organized, Turkey has drifted away from America, and the new Iraqi/Afghan governments are from all appearances semi-hostile towards America.
