All of those claims are true.
We can describe positive temperatures such as room temperature (20 degrees C = 68 degrees F), and we can have negative temperatures as well (eg: -40 degrees C = -40 degrees F). The only time we cannot have negative temperature is when you use the Kelvin temperature scale. This is because absolute 0 represents the coldest possible temperature in the universe. In more common settings, Celsius and Fahrenheit are frequently used.
Debt and money are often involving negative integers. If we were to write -7 in terms of money, then it could represent a person owing $7. Positive values represent having the actual money and not being in debt.
When it comes to elevations, positive integers represent being above sea level; while negative values are below sea level. For example, Mount Everest is +29035 above sea level (or simply 29035 ft) and the Mariana Trench roughly has an elevation of -36201 ft (meaning it's about 36201 ft below sea level).