Rule 621 High Sticks

Team A has a player trapped deep in the Attacking Zone when a Team A player shoots the puck into the zone. The Linesman correctly signals a delayed off-side. A Team B player plays the puck with the blade of his stick two feet over his head, and he is the next player to play the puck. The Referee stops play with the puck in the Defending Zone and the off-side Team A player still in the zone.

Where is the face-off?

At the nearest Neutral Zone face-off spot. Rule References 621(c) and 630(d).
Even though the puck was played with a high stick, the original infraction was off-sides.

Rule 612 Face-Off Locations

A stoppage of play in the Defending Zone was caused by a defending player and the Official assessed the defending team a penalty. Subsequently, during the same stoppage of play, an attacking player is assessed a penalty. Where is the ensuing face-off?

At the nearest Neutral Zone face-off spot. Rule Reference 612(c).

The stoppage of play was not caused by the actions of players from both teams for the purpose of establishing a last play face-off. The penalty by the attacking player causes the face- off to occur at the nearest Neutral Zone face-off spot.

Rule 501 Appointment of Officials

An On-Ice Official arrives at the game only to realize that he forgot his helmet. Is he allowed to officiate in this instance without a helmet?

No. Rule Reference 501(c).

All On-Ice Officials must wear a hockey helmet when officiating. Under no circumstances should an official be allowed to participate without this required piece of protective equipment.