Simple-dynamics conjectures for Newton maps of real polynomial maps

Let $f:\mathbb{R}^2\to\mathbb{R}^2$ be a polynomial map of degree $n\geq3$ with $n$ distinct real roots $\{c_i\}$. Let $N_f$ be its Newton map, $J_{N_f}$ its Julia set, $F_{N_f}$ its Fatou set, and $\mathcal{F}_{N_f}(c_i)$ the basin of attraction of $c_i$.

Simple-dynamics conjectures. The following properties hold:

1. $J_{N_f}$ is the countable union of wedge sums of a countable number of circles and of Cantor sets of circles of measure zero.
2. $F_{N_f}$ has no wandering domains.
3. The union of the basins of attraction $\mathcal{F}_{N_f}(c_i)$ has full Lebesgue measure.
4. Every neighborhood of any point of $J_{N_f}$ contains points from at least two distinct basins of attraction.
5. Unlike the holomorphic case:
6. basins of attraction are not necessarily simply connected;
7. immediate basins of attraction are not necessarily unbounded;
8. $J_{N_f}$ can have interior points without being equal to the whole $\mathbb{R}\mathrm{P}^2$.

These are proposed as two-dimensional analogues of Barna's theorem and related one-dimensional results for real Newton maps. The supplied parser gives no evidence that these claims have been resolved.