$S1$ is equivalent to "every infinite set is Dedekind-infinite", so $\sf ZF<ZF+(S1)$, because it is consistent that infinite Dedekind-finite sets exist.

$\sf ZF+(S1)<ZF+(S2)$ follows using results from [this answer](https://math.stackexchange.com/questions/393196/the-relationship-of-frak-mm-m-to-ac), which implies that $\sf DC_\kappa$ doesn't imply $S2$, and hence nonexistence of infinite Dedekind-finite sets, which is a corollary to $\sf DC(=DC_\omega)$.