As a senior pay-as-you-go mobile phone user (Tesco), I seek some simple advice.

Planning a short holiday in the US and wish to use my U.K. phone for local / emergency calls only - i.e. access required to a US provider; calls + txt, but no data requirement. Long distance / overseas call calls if required will use a locally acquired US prepaid card, but still requires a local call to access a US provider as above.

Seen many on-line advertising offers, but somewhat confused due to the vast range of technicalities and marketing hype.

Phone type: Doro 6520, is this compatible with the US phone system?

Can I obtain a replacement / second SIM card or overseas roaming option for my phone? If so, from whom, where, and how obtained. U.K. or US purchase?
min cost ~ £20.

I googled your phone and it works on 1900Mhz, which is compatible with several US networks. My advice would be to get a pay as you go sim from Three. Forward all your calls to that number, then put the three sim in your phone. Now you can still receive calls as normal without having to give out a new number, but outgoing calls will come from the Three SIM card.

Three will allow you to use your phone in the US to make and receive calls to and from the UK for no charge (feel at home)
If you need to make a call to the US (or anywhere else) you can use a UK based calling card (Tesco for example). It’s ironic that it’s cheaper to bounce a call twice across the pond than to make a local call in the US, but everything goes through the internet nowadays anyway.

Thanks for the education rs. Three appears to offer what I require, although there are still some aspect which need further clarification; at least I’m up and running