What is the convention that we take for the interior product of a function?
i.e., if $X\in\mathfrak{X}(M)$ and $f\in C^\infty(M)$, how do we define $\iota(x)f$?
Recall that $\iota(X)\alpha := \alpha(X,\cdot)$ for $\alpha\in\Omega^r(M)$ and then $\iota(X)\alpha\in\Omega^{r-1}(M)$ but this doesn't make sense for $f$.
I suppose that we take the convention that $\iota(X)f$ is zero.
Yes, the convention is that $\iota(X)f = 0$ for all functions $f$.
One nice feature of this convention is that it allows us to say that $(\iota_X \circ \iota_X)(\alpha) = 0$ for all $\alpha \in \Omega^r(X)$ for all $r \geq 0$ (rather than just $r \geq 2$).