Coaster Brake Newb: Help?

Has a tensioning arm, all in place and bolted tight to its bracket, it's an unbranded hub so probably made of an old Aldi sardine tin.

Should the sprocket spin all the way round if you spun it with your hand? On my wheel, the sprocket moves so far forward > stops. And so far backwards > stops. All smooth and no grittyness, but is this normal at all?

They have a bit between braking and going which does nothing, it's hard to explain but with most it has some cone shaped bits inside that move along and either press against the outside of the hub to brake or lock into the center of the hub to go and then between is a gap.

While it is going it should feel just like a normal freewheel'd hub.