Mufasa - Bioelectrical impedance devices measure the body’s resistance to an electrical current. If you look at a Tanita scale, you see 4 metallic electrodes. Two of those electrodes generate a voltage and two of the elctrodes measure the residual voltage which is left over after passing through the body. The ratio between the starting and ending voltages is impedance. To figure out how to convert impedance values into a percent body fat, validation studies were done with Hydrostatic weighing or preferably multi-compartment body composition models. Thus teh impedance value along with things like weight, height, and sex were used to create a coplicated algorithm which converts all these factors into a %body fat. OK, that may sound reasonable, but here are some problems that we run into when we use these scales.
The problems are primarily affected by changes in total body water (TBW). TBW is assumed to be about 73% of your fat free mass (FFM). Any changes to this quantity of water or to its electrolyte content will change your impedance and thus change your value for %body fat. So you answer to question #1 is that these devices really don't do either of your suggestions, but they clearly do not measure fat directly. In reality, it is much more like the second answer because most of the changes that cause the machines to vary occur in the FFM compartment. Basically if you assume that this device is measuring your TBW, and that TBW is 73% of your FFM, it calculates FFM and subtracts that value from your body weight leaving you with a measure of your fat mass (FM). FM/Body weight = %body fat.
Impedance can also be altered by changes in skin temperature, skin moisture, body posture and much more. So to get the most reliability, you need to find the time of day where your skin temperature, TBW, skin moisture is the most consistent. If you don't work out in the morning, then it is pretty easy. If you have a Tanita scale, wake up, go to the bathroom and hop on with no clothes on or with the same type of clothing on every single time. Clothes add to your weight and thus could artificially change the values. After you have this measure, get another measure after you have taken a shower in the morning and have completely dried off (hair also). Track the reliability over a couple of weeks and then just use the one with less variability.
In response to question #2, the more fat you lose, the more homogenous your body becomes. Impendance works great when measuring simple homogenous solutions which are evenly distributed. Humans are clearly not an evenly distributed homogenous solution. Thus if you get rid of fat and increase muscle mass and body water, you move towards a more evenly distributed homogenous structure. Just an idea. Let me know if you have other questions and if you are looking for a way to figure out when to use the scale, let me know a few details about your training schedule and diet.