-Luminosity is the term for brightness reading in lux, footcandle or similar units. The brightness is read by a small sensor so, yes, it is a single point reading.
-There is no such thing as a lumen meter; total lumen is read by a luminosity sensor while the sensor and light are placed inside an integration sphere that reflects all of the light being emitted.
-I calibrate light meters and by experience, although there are no actual standards on the general calibration of such devices except for certain specific scientific applications, they are all pretty much as accurate unless you're going to buy a flat-spectrum 10 000$ machine (which will also read both UV and IR and not really give a representative figure). Some have an integrated sensor (i.e. the sensor is part of the unit) and others have a sensor attached by a wire. The latter is a little more convenient as you can have the sensor mounted on a rig or integration sphere and still read it with ease, but they are slightly more expensive. Sensor sizes do vary. I would suggest a larger sensor for integration spheres and a smaller one for single-point measurements, although it might not make much of a difference in the end.
[EDIT]:
I just realized I said something a bit stupid: Light meters are by convention calibrated using a ~2700K bulb and an IR filter (usually halogen and I gotta double-check that kelvin statement if I can find the paper. I'll update this post if I do find it.) I also have an LED source to calibrate some meters and, though all meters give pretty much the same reading with the incan bulb, the readings can differ greatly when using an LED source. An educated guess would mean that the cooler the LED, the more the readings can differ. Most sensors include an UV filter and only the more recent ones (don't ask for a date, could go as far back as 10 years for all I know) include an IR filter. The IR filter can make quite a difference on the reading for both incan and LED. [/EDIT]
