Bicliques for permutations
A sliced biclique over $g$ is two set of states ${Q_{i,j}}$ and ${P_{i,j}}$ such that for every pair $(i,j)$
$$
P_{i,j} = Q_{i,j}.
$$
The states are chosen so that the difference between $Q_{i,j}$ for fixed $i$ is small, and the same must hold for $P_{i,j}$ and fixed $j$.

$Q$ and $P$ map to the same hash value $H$, but it is not state #13, but rather
$$
H = \#1\oplus\#13.
$$
You use this equation to filter out incompatible pairs $(i,j)$. The entire trick is to treat some $Q$ as the same, and similarly with $P$ to reduce the computations.

So to answer your other questions

2) Right

3) These are the numbers of recomputed S-boxes in each round from 1 to 6th. There are $6*64 = 384$ S-boxes in total, so there must be $2^{-2}$ calls, not $2^{-3}$.