Why does the order of 人口 change? One of the first questions in my book is 你家有几口人？ But the book highlights the word "人口" as people. Why does it change? Is it because 口 is the measure word for 人? Could you say 三口人口? When do you use each form?
You're right that 口 is one of the measure words for 人, but 人 (people/person) and 人口 (population) are two different words. The word 人口 is mostly used for the population of a city or a country instead of a household.

You can say 几口人 (how many 'units' of people), 三口人 (three 'units' of people), but not 三口人口 (three 'units' of population).