As far as the second point, if that was the case, then it wouldn't be a balanced field length would it? I mean, I guess in theory you could have a balanced field length that was longer than the actual runway, but that wouldn't be very practical either as in the case of a reject you would run off the end every time.
Performance was a real weak area at my former company. I tried to change what I could when I was in a position to bolster that.
The BFL is purely based on a set number of feet. Let's say that number for this discussion is 7000'. So now all the numbers need to line up to get the airplane either: a) Accelerated to V1 and stopped in 7000' or b) Accelerated and continue the take off to the screen height by 7000'
For our hypothetical airplane, we'll say the brakes take 3500' to stop the airplane, so obviously the V1 must reflect that distance. We'll say our performance numbers come up with 105 kts for this number.
Our hypothetical airplane has a second segment issue, so we'll used a reduce takeoff flap setting, say flaps 5 instead of 10. Through our performance machinations, we figure out that to get the airplane to screen height in 7000' we can used a reduced flap setting, but we are also using a reduced thrust setting for T/O. Due to the lower amount of flaps set, we don't rotate the airplane until 115 kts.
So, V1 is 105, Vr is 115. We have two different speeds, yet both allow the airplane to use balanced field because both requirements are met in the same distance.
Now, where does unbalanced field length benefit?
We know that we need 7000' to go or stop the airplane at the given weight from the previous example - and to prevent any other machinations, the environment is the same (ISA and same Field Elevation and 0 slope on any runway).
Well, now we find ourselves at some outstation with one short runway - 6500 feet for this example, however there is a clear way (the departure end of the runway ends and there is a body of infinite water in that direction).
The FARs allow us to take a "Clear way" credit as there are no obstructions on a specified clearance plane (My brain says at a 1.25% gradient for some reason - but that's a recall). We know it takes 3500 feet to stop the airplane, and 7000 feet to get to 35'.
So what we do in this instance is reverse engineer to the 3500'-to-go distance on the runway. Using our performance computations, we figure out what speed we'll be at that point in space, say 95 kts. Obviously we know we need 115 kts to fly the airplane.
So in this instance 95 kts is our reject speed, based on available runway, and our Vr remains at 115. We are still able to carry the same weight as we were off of the 7000' runway.
I hope this makes sense.