1/ How is it that float type carburettors meter fuel by volume and not mass.
QJB, while it would be wonderful for a simple device such as a float carburetor to be able to differentiate between fuel densities and therefore meter by mass rather than volume, it just isn't in the cards. While you're correct that the carburetor does meter by pressure differential, you're also incorrect that the metering which takes place does not change with altitude. It does.
How much it changes, of course, depends on the altitude and ambient conditions, as well as the operating condition of the engine, and of course the type of engine. It's for this reason that pressure carburetors were developed long ago as aircraft flew higher and higher...along with ignition systems designed to operate at higher altitudes (low tension ignition, pressurized mags, etc). The float carburetor using only ambient pressure and venturi pressure as the motive function to move fuel into the slipstream works well, but is subject to change and error as those values change.
The relationship between ambient pressure loss and the velocity of airflow through the engine (and the mass of that airflow) is not linear during the climb to altitude. It's affected both by ambient conditons and by the engine efficiency. Remember that the engine is a big suction machine so far as the carburetion is concerned, drawing air though the induction (and thus fuel along with it). How efficiently it can continue to do this as the aircraft climbs, especially in a normally aspirated powerplant, will determine in part the relationship between the venturi jet and the calibrated air leakage vent into the carburetor float bowl.
If there were no change in the relationship between the venturi jet and the float bowl pressures as the aircraft climbs, then of course there would be no change in the way fuel is metered...but it doesn't work that way.
I think what you're really asking about is the volumetric vs. mass change in airflow with the change in altitude, is that correct? That is, if ambient pressure drops in the float chamber, and the air flowing through the venturi is less dense due to an altitude increase, how does this affect fuel flow? Your question appears to ask specifically regarding the mass vs. volume of fuel, rather than air...and the truth is that it can only measure by volume of fuel...density and therefore mass will change with temperature, but it's strictly a volumetric disbursement into the carburetor throat because it's being drawn using a preset jet and passageway...it's measured and metered only by volume. The change in airflow values (volume vs. density) do produce changes in the relative pressure differentials...and thus changes in the volume of fuel that's metered.
The simple explanation is always that it's the drop in air density that requires leaning of the engine as we climb. This is, of course, true. But there's more to it, and the fact is that even in cruise at altitude we need to re-lean the engine, or readjust the mixture, if a throttle change is made. We also need to readjust the mixture in the event an airspeed change is made, even with a constant RPM setting...mixture should be readjusted anytime altitude, airspeed, or power setting changes...these all affect the differential pressure in varying degrees, as well as air density (mass), and thus mixture.
2/ Why is it that increasing volumetric efficiency reduces Brake Specific Fuel Consumption.
Let me pose a counter-question to you in response: why is it that a smoker has to work harder to climb a mountain than a non-smoker, assuming the same general physical condition, age, etc? Part of the answer to the imperfect example is that of volumetric efficiency.
Allow a person to breathe better and they don't have to work as hard to do something, and an engine is little different. The harder the engine struggles to take a breath, so to speak, the more energy is consumed trying to aspirate itself, and the less energy is expended on actually performing work. Much of a piston engine's power is lost to internal friction, which takes many forms...volumetric inefficiency is one such form.
Another point of view on the same subject is the amount of power the engine is able to produce given it's displacement, weight, etc. Obviously an engine sitting at idle is producing little power, and able to do little work. Open up the throttle and go fly, however, and now the efficiency of the engine may be said to have increased (subject to a particular measurement or quantification, of course). Increasing the throttle is an example of increasing volumetric efficiency, though again, an imperfect example because we're not actually changing the opening into the cylinder (such as giving it a bigger intake valve head, for example)...but you can see a distinct disparity between work performed sitting at idle on the ramp, and roaring overhead at 300 knots. By the same token, modification to the cylinder itself, or the induction, by increasing the amount of airflow into the cylinder vs. that which it's capable of handling in a given cycle, will improve that of which the engine is capable, and ultimately make it more efficient.
Decrease the intake valve size, block the induction, or by other means reduce the volumetric efficiency of that particular cylinder or engine, and the engine will struggle inefficiently to do the same work it did before...and it's efficiency will decrease.