First of all, congratulations. International experience is invaluable for an American (assuming you’re native born) provided you keep an open mind and are willing to view change as an adventure. It broadens your horizons immensely. Increasingly, international tax issues and banking are very much a part of that adventure. Given the gravity of an international relocation, it’s often one of the last things considered when making the move. I believe you’re wise in considering the implications at this time.
I am somewhat surprised that your company does not have provisions for tax assistance already established (again, an assumption on my part that the company already has a UK base). At minimum, an established rapport with a US/UK advisor would be expected, leaving the individual to work with that advisor independently. If they do not, your adventure has just been heightened, but that certainly is not an unusual situation for many to be in.
It must be accepted that ALL income and benefits, from anywhere in the world and how ever derived, will be taxed by the US if you are a US citizen or green card holder. There are few exceptions.
I’ll leave the California State situation to those with more personal experience, but the California Treasury’s web site is a good place to start.
Purchasing Private Health Insurance in the UK is a purely personal choice. Many people do have a private plan in addition to NHS coverage, but I wouldn’t call it the norm for the average UK citizen.
As regards the Totalization Agreement, the following is a self-explanatory link which should answer most of your questions.
http://www.ssa.gov/international/Agreement_Pamphlets/uk.html