For temperatures, zero is an arbitrary reference point, depending on which scale is used. For Celsius, zero is assigned the the temperature at which water freezes. So temperatures which are colder than this temperature will be negative values, and temperatures warmer will be positive values. Fahrenheit uses a different reference point for zero, but similar principles apply.
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A mercury thermometer is used to measure temperature.
Use a thermometer.
Every aspect of mathematics depends upon integers, and even if you don't do any mathematics, you count things with integers. If you even want to know how many guests you are having for dinner, you need to use integers.
You can sometime use integers but often speed or velocity can also be irrational.
Yep.