"Question: should I expect my BAS to cut through 4 inch branches with one swoop?"
Depends. If you've got muscles like Arnie's big brother and you were born on the planet Krypton - well, you probably won't bust the knife trying. If you're an ordinary mortal like us folks, no. Expect the same level of cutting power as you'd get with a tomahawk or hatchet. Practice will improve your technique.
"Also, how should I go about sharpening my khukri"
I suspect there's as many answers to this as there are forumites. In my case; if the blade's just dull (ie no longer sharp enough to shave a hair or two off your arm) hone it with the chakma provided or some other piece of hard steel; I use a tungsten carbide lathe tool. If it's gotten very blunt, I use fine-grade slipstones and an India (oil) stone, followed by stropping on leather, followed by steel. Burnishing the edge with the chakma means you aren't removing metal every time you sharpen; you're just putting the edge back in shape. Br careful when sharpening to follow the cannel (slightly convex) profile of the edge - if you sharpen it like a conventional hollow- or flat-ground edge, you'll reduce the khuk's cutting ability. I think it was Yvsa who said, "Sharpen it like an axe, not a knife".
Not that it'll need sharpening all that often...