It sounds like your numbers and reasoning are pretty much on track. I use 4.24 lbs per gallon as the weight of propane but 4.25 is close enough.
Your 38 gallon tank is theoretically capable of holding 38 gallons. However, you want to burn the propane gas, not the liquid and you need some room for the gas to be held as it evaporates off of the liquid. That's why you only fill to 80%. Assuming that your tank is perfectly installed (most are close, but not exact) the bleeder valve should be able to detect when the liquid gets to the 80% mark so that the refueler can shut off the propane flow into the tank. At that point you would have 80% of 38 gallons, which is 30.4 gallons. At 4.24 pounds per gallon that should give you 128.9 pounds of propane that you can burn.
The propane gas is pressurized as it boils off the liquid propane. Just as in a radiator, increasing the pressure raises the boiling point. So, as the gas leaves the tank, the pressure reduces, and more liquid propane evaporates into gas. The problem occurs when your LP tank gets down to around 10-20% full. There's plenty of room for gas but not a whole lot of liquid left and the gas pressure drops off, especially when the tank is cold. You will find that your LP furnace, genset, or other applinaces aren't burning too well when the propane gets low. So, in theory, you have 80%, or 30.4 gallons in your case, to use. But, in actuality you won't want to take it down that far so I wouldn't count on that much runtime.
Your calculations on propane usage in your genset appear to be correct. Remember that the propane consumption will vary as to how much load you are running on the genset but that appears to be a good average.
Tank gauges are not all that accurate. They're based upon a float lever, not that unlike a regular gas tank gauge, so they are subject to slight variances. I've refilled and did the math and sometimes what I expected to put in, based upon the tank gauge's reading, wasn't what the pump meter came up with.