$L_p(X, \mu, E)$ where $E$ is a Banach space: reflexivity, separability, duality, and uniform convexity

Question

At page 103 of Brezis's Functional Analysis there is

The following table summarizes the main properties of the space $L_p(X, \mu, \mathbb R)$ when $X$ is a measurable subset of $\mathbb{R}^N$ : $$ \begin{array}{|c|c|c|c|} \hline & Reflexive & Separable & Dual space \\ \hline L^p \textit{ with } 1<p<\infty & YES & YES & L^{q} \\ \hline L^1 & NO & YES & L^{\infty} \\ \hline L^{\infty} & NO & NO & \textit{Strictly bigger than } L^1 \\ \hline \end{array} $$

Here $p^{-1}+q^{-1}=1$. I would like to make an analogue for Banach spaces.

Let $(X, \mathcal A, \mu)$ be a $\sigma$-finite measure space and $(E, |\cdot|)$ a Banach space. Fix $p \in [1, \infty)$. Let $L_p := L_p (X, \mu, E)$ and $\|\cdot\|_{L_p}$ be its norm. Here we use the Bochner integral. Then

1. If $p \in (1, \infty)$ and $E$ reflexive, then so is $L_p$.
2. If the $\sigma$-algebra $\mathcal A$ is countably generated and $E$ separable, then $L_p$ is separable.
3. $L_{p}(X, \mu, E)^{*}=L_{q}(X, \mu, E^{*})$ IFF $X^{*}$ has the Radon-Nikodým property with respect to $\mu$.
4. If $p \in (1, \infty)$, then $L_p$ is uniformly convex IFF $E$ is uniformly convex.

I'm happy to receive your correction and suggestion!