Thank you for the reassurance. I was going crazy researching this. What had confused me was the scenario when the US mobile phones were physically in a different country. No other websites were clear on that.
About the US phone to UK phone scenario, thank you for the clarification that there may be two ways to dial UK numbers; that explains why I saw contradictory info on other websites. Also in US phone to UK phone, I need to leave out any initial zeroes in the UK number, correct?
I just realized I left out one other permutation for you to double-check me on — but I think I’m right here:
From US mobile phone (in UK) back to the US: 011 (or plus sign)1 xxx-xxxx
Am I right on those?