Structure of singular superalgebras with $2$-dimensional even part and new examples of singular superalgebras

It is proved that a singular superalgebra with a $2$-dimensional even part is isomorphic to a superalgebra $B_{2\mid3}(\varphi,\xi,\psi)$. In particular, there do not exist infinite-dimensional simple singular superalgebra with a $2$-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number $N\geq 5$, except the numbers $6,7,8,11$, there exist singular superalgebras with a switch of dimension $N$. For the numbers $N=6,7,8,11$, there do not exist singular $N$-dimensional superalgebras with a switch.