B777 First Officer reported battery powered wheelchair documents contained errors and also missing required Hazmat labels.

Narrative

Prior to departure in ZZZ on my captain OE (Operational Evaluation); a gate agent entered the cockpit and presented me with a Battery Powered Wheelchair or Mobility Device Tag form. The form was filled out to indicate a Dry-Cell/Non-Spillable battery; which according to the form (if the wheelchair is collapsable); requires the battery to be removed and placed in a strong rigid outer package marked as 'non-spillable battery not-restricted'. I returned to the gate area and spoke with both the agents and the passenger; and verified that the battery was a Nickel Metal Hydride dry cell battery. The passenger had been told by reservations; the mobility desk and the agents that she should carry the battery with her on board the aircraft; in direct conflict with our form and the DG (Dangerous Goods) Chapter of the FOM. In fact; the agent had written 'battery at seat' on the form next to the verbiage that required it to be in the cargo compartment. After discussion with the agents and the passenger; it was agreed that the battery would be boxed and carried in the cargo compartment; with the appropriate 'non-spillable battery non-restricted' marked on the box. Upon arrival in ZZZ; I ensured that the wheelchair and battery were returned to the passenger. I also noted that the agents had failed to mark the box as requested and required.