$S1$ 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, which implies that $\sf DC_\kappa$ doesn't imply $S2$, and hence nonexistence of infinite Dedekind-finite sets, which is a corollary to $\sf DC(=DC_\omega)$.
