What are the best books to selfteach these? I want to develop better intuition in econometrics...
linear algebra & calculus?

Stewart and Spivak's calculus texts are common and popular. It you want more, Loomis and Sternberg's book is free online, and it covers everything. As for linear algebra, just pick up a Schaum's guide. Though, you can probably get through a lot of Greene just by knowing matrix algebra, continuity arguments, and derivatives.

Not so sure about the car analogy. Maybe it's more like knowing how to read a map? If you're just going the same places the same way every day, it's probably fine to not know how maps work, but if you want to go somewhere new, you'd better understand maps.
Or to stretch the analogy further you can rely on GPS and drive yourself into a cow pasture.