Simmer? Leave pan where you were heating it, and turn the gas/electricity as low as it will go, the picture shows tiny little points of bubble forming, that's about right. Silas says to remove from heat altogether, and if you are somewhere warmish (not up a big hill!) that will probably be fine, especially if the pan is a large and/or thick one.

How long in LCP? Well, like with boiled eggs, individual taste varies. To start I would suggest your normal preferred time for boiling, plus maybe 30 seconds if the LCP is particularly thick, 60 seconds for a ramekin. Adjust as experience grows.

I believe that our nearest equivalent to what the States know as an English muffin would be a plain teacake, bap, breadroll, stottie (there have been previous threads on further names).

Unless you get your eggs at the farm gate they are probably 4+ days old when you receive them. My earlier post suggests a way of assessing those you have. If you have had an egg a week, then it is at least one week old (obvious I know, but sometimes overlooked).

Google will take you to sorrel, there's a good chance it is growing wild somewhere near you if you are in the UK.