Why aren't house prices included in CPI?
The CPI stands for a Consumer Price Index. As in the price of things that are consumed (at a particular moment in time). Real estate prices are not the price of something consumed because they contain the value of current housing consumption but also the capitalized value of future housing consumption. As such, including house prices would make the CPI a mixture of consumption at different times, and therefore unsuitable for comparing the price of consumption bundles at distinct times. Instead, they use a purer measure of the price of housing consumption: rents. 

Rents reflect the price of consuming a flow of real estate services at a moment in time. Of course, many homes are owned by the occupants and not rented. Therefore, the calculators of national accounts generate something called "owner occupied rents", which is an attempt to calculate what the rents would be on homes that are occupied by their owners. This measure has problems, but for many purposes is quite adequate (Crone, Nakamura, Voith (2004)).