Why is a mile exactly 1.609344 km?
Because that is its definition, fixed by the international yard and pound agreement of 1959. The tool uses definitions, not rounded factors, so every digit is there.
US cups or imperial cups?
Both are in the list, marked US and imp, since the two share a name; the same goes for gallons, pints and fluid ounces.
How is temperature converted?
By formula rather than by a factor, because Celsius and Fahrenheit do not share a zero, and the formula line shows the whole of it. Fuel economy works the same way, since litres per 100 km and miles per gallon run in opposite directions.
What do significant figures do?
They set how many digits the result keeps: at 3, a metre is 3.28 feet; at 6, it is 3.28084. A whole number stays whole whatever the setting.