Concerning your second remark in red, "where s came from," it's probably a typo at this point. I would not worry about this.

The third remark in red is about an example of simplifying a DNF. It's not necessary to replace p /\ q by s; you can just replace back s with p /\ q in every line there. The point is that one can replace a part of an expression that matches the left-hand side of an equivalence like p /\ (q \/ r) <-> (p /\ q) \/ (p /\ r) with the right-hand side (or vice versa). The intention is a serious of rewrites is to make the original DNF expression simpler.