Rule 639 - Tripping

A defending player leaves their feet and slides into the puck carrier. The defending player gains possession of the puck and the attacking player falls to the ice after being hit by the defending player’s body. Should a penalty be assessed?

Yes. Rule Reference 639(Note 3 and a).

When a player leaves their feet and slides into an opponent, thereby causing them to fall, a penalty for tripping must be called regardless of who gains possession of the puck. The only exception is when a player drops to their knees to block a shot and their momentum carries them into the player
shooting the puck, causing them to fall. In that event, no penalty is to be assessed

Rule 624 - Icing the Puck

The puck, shot from behind the center red line, bounces over the stick of an opposing player who attempts to play the puck or rebounds off the boards and over their stick. Is icing still in effect?

Yes. Rule References 624(a and b.5).

The Official must make their decision based upon the proximity of the puck to the player, the speed of the puck, and whether or not the defending player had a reasonable opportunity [emphasis added] to play the puck

 Rule 615 - Fighting

Two players on the same team become involved in a fight with each other during a game. What penalties, if any, shall be assessed?

If the fight occurs on the ice, both players shall be assessed a game misconduct penalty and the offending team shall be assessed a bench minor penalty for delaying the game. If the fight occurs off the ice, both players shall be assessed a game misconduct penalty. Rule References 615(a and b) and 610(h).

It is not feasible to assess the two players each a major and a game misconduct penalty, because the team would have to play short-handed by two players for five minutes. Likewise, a “first to intervene” penalty would not apply to a player on the same team who attempts to break up the fight