It sounds as though you do have a permanent built-in tank with the usual sender mounted on the dial gauge. You should be able to see the pointer on the gauge despite the sender being on top of it if you look closely enough.
The three light gauges (often they do have four lights, but the bottom light is always on so there are only three that do anything) are accurate for propane but not at all precise. In other words, the points where it changes from full to 2/3 to 1/3 to empty are pretty repeatable and usually reasonably calibrated, but there's a lot of room between each step. The readings for the black tank, on the other hand, are often both inaccurate and imprecise.
The fridge uses not much propane at all, maybe a pound a day as a very rough rule of thumb (and probably a bit less than that). A year ago I took an extended trip to Alaska, 2 and a half months, and went through about two tanks of propane (with a built-in tank, not cylinders) for the entire trip.
