How does amine inversion affect basicity?
Amine inversion is also known as nitrogen inversion. You can find more here: http://en.wikipedia.org/wiki/Nitrogen_inversion

It has nothing to do with relative basicity of amines, that is defined by 1) energy of particular N-H  bonding (increases with +I effect) and 2) energy of ammonium cation hydration. (decreases with alkyl group number and their size). The relative balance of said factors is fragile and cannot be easily predicted without reference to experimental data except cases when amine has lone pair involved into bonding interactions (aniline, pyrrole, amides) or connected with extremely strong electron acceptors.