How do we know $\dot{\hat{\phi}}$ is in the direction of $-\hat{r}$?

See above question for the argument for why $\dot{\hat{\phi}}$ is perpendicular to $\hat{\phi}$. The vector $\hat{\phi}$ is tangential to the circle at radius $\vec{r}$. The vector perpendicular to the tangent is in the radial direction $\hat{r}$.