Do Schwann cells have Na+/K+ ATPase pump?
Yes. Although utilizing the action potential is not in their function, Schwann cells do have Na/K ATPases. In fact all animal cells do. It contributes to the resting membrane potential in neural networks, with regards to Schwann cells, and prevent differences in osmotic pressure from disrupting the cells.

As for your second question, action potentials do not occur in Schwann cells as there is nowhere for this "impulse" to travel to. A localized depolarization is not an action potential. Papers such as this, and this suggest that voltage-gated ion channels in Schwann cells serve complex and specific purposes such as inducing myelin formation.