1) There is a correspondence, but there are more restrictions on YT than in the case of $SU(N)$ where the restriction is not to have more than N-1 boxes in a column. Due to an additional invariant tensor, metric $\delta^{ab}$, we can take traces and irreducible tensors need to be traceless. Combining it with the $\epsilon$-symbol you get that the total height of the first two columns has to be not greater than $N$, otherwise the tensor is identically zero.

2) There is a generalization of the Hook formula that works for $SU(N)$. The details can be found in this old paper.

3) Again there is an algorithm, which is a superposition of two $SU(N)$ tensor product rules. One has to take into account traces. The precise formulas are the very first in this paper