Mortgages with low interest rates are also one of the (main) reasons houses are so "expensive" in the first place.
The cheaper money (credit) is, the "higher" the prices will go.
It's not so much that houses became expensive, it's more that money to buy a house (specifically mortgages) became relatively cheaper. Low interest rates did that.
This is a one-time effect, though. Or at least, an effect that only changes periodically (and should reverse) when interest rates change. 30-year mortgages have been standard in the US for most of my life, and houses have gotten a lot more expensive during that time.
House size, build "quality" (the details in the house), resource scarcity, and zoning policy are the drivers of cost. Cheap credit and lifetime loans allow the system to continue.
I don't know about this - when I see quotes on build cost in my area they add up to more than similar properties sell for in some cases, and generally aren't a whole lot different than buying to the point that I've wondered why it's like that.