E brake on a Mercedes

"Also in the UK , and I'm guessing elsewhere, its not only not called the emergency brake , but people have never even considered that that is its purpose. We thought it was to stop the car rolling away when you parked it."

I think it's "officially" called a "parking brake" now in the US too. Most people still call it an emergency brake, or e-brake for short, at least the people I know do (I don't know what younger people around here call it).

"I guess the proportions of auto vs manual being opposite in US compared to elsewhere might be why."

Yeah, automatics have been more common than standards in the US since at least the 1960s, unfortunately, and with new vehicles, they are practically extinct in the US. I much prefer a standard transmission.

"I was under the impression brake master cylinders had duel pistons or something to guard against sudden brake failure."

They do, but they haven't always. Dual piston master cylinders became mandatory in 1967 in the US. The front brakes are controlled by one piston and the rear brakes are controlled by the other piston, so if, e.g., one brake line breaks, you will still have either front or rear brakes.

It makes a sudden total brake failure less likely, but it can still happen. For example, the linkage between your brake pedal and master cylinder could break and then there would be no way to apply the brakes, despite there being nothing wrong with the rest of the brake system. Or, your distribution block could burst, and since both the front and rear brake lines go into that block, you'd have no brakes at all. Of, if your car is rusty, all of your brake lines could be rusted to the point where they are about to fail, so one in the rear could fail and then immediately after that one in the front could fail too. Also, if your firewall is rusty, the part that your master cylinder (or power booster) is bolted to could fail, and that would have the same effect as your brake pedal linkage breaking. Or, your entire master cylinder could seize up or suddenly spring a big leak that affects both chambers.

Emergency brakes are cable-operated so they work independently of the hydraulic brake system.

Ah. I thought this was a new (old) thing.

I recently discovered I don't think I can control that brake manually. On a hill, I was wondering how I could roll the car or if both batteries were dead, how to activate or release that brake?
They should go back to some kinda of manual. They won't. Oh well.