Seed's conjectures on reduced Szabó homology and its spectral sequence

Let $\operatorname{\mathcal{D}}$ be a link diagram, let $p$ and $p'$ be points that are not double points of $\operatorname{\mathcal{D}}$, and let $\widetilde{\operatorname{CSz}}(\operatorname{\mathcal{D}},p)$ denote Szabó homology reduced at $p$. Let $E^k$ be the Leray spectral sequence from the homological filtration on $\operatorname{CSz}(\operatorname{\mathcal{D}})$, and let $\widetilde{E}^k$ be the corresponding spectral sequence on $\widetilde{\operatorname{CSz}}(\operatorname{\mathcal{D}},p)$. The notation $\{\pm1\}$ denotes a shift in quantum grading. Seed's conjectures.

1. $\widetilde{\operatorname{CSz}}(\operatorname{\mathcal{D}},p) \cong \widetilde{\operatorname{CSz}}(\operatorname{\mathcal{D}},p')$.
2. (Twin arrows)

$$E^k(\operatorname{\mathcal{D}}) \cong \widetilde{E}^k(L)\{-1\} \oplus \widetilde{E}^k(L)\{1\}.$$

3. If $K$ is a knot, then $E^k(K)$ is invariant under mutation for $k \geq 2$.
4. Szabó homology is isomorphic to mirror Szabó homology.

These conjectures are presented as further conjectures motivated by Seed's computations and the preceding Szabó–Heegaard Floer conjecture; the source does not report a resolution.