I think Internal or Interior Forces is better. Like Sfc said, they belong Ministry of Interior (Internal Affairs is too literal). From their website, they have an infantry division and some support units these days.More like "Internal Forces" if you want a literal translation. The Russians actually use the word Armija (though spelled in Cyrillic, of course) for "Army." So -- when you see "CA" on their stuff it stood for Sov'jetskaya Armija / "Soviet Army. Probably a better translation of your patch would be "Domestic Forces." Say that a couple of times and tell me you can't imagine someone inventing the organization to match it here in the USA. I'm betting you can. And if you find that a bit unnerving, I say good for you. The Soviets played the name game very well. So to properly translate their propaganda requires, in my view, a similar creep factor in English.
Yes and no. When the Soviet Union disintegrated in 1991, the Border Forces were part of KGB. Today they are part of FSB which is reorganized KGB. They have been part of Ministry of Interior from 1953 to 1957.I think the Pogranichniki or border forces were part of the organization too, and probably still are. This force was always pretty disciplined, and make our border patrol look like Walmart greeters.