618 - Handling Puck With Hands

What guidelines should be followed in allowing a player to catch the puck and immediately drop it?

The motion of catching, then dropping the puck, must be virtually one continuous motion. Rule Reference 618(a).

Provided the player catches the puck and drops it to their stick in one continuous motion, play should be allowed to continue.

However, if they hold the puck for any length of time, take one or two strides with the puck, throws the puck to an area away from their stick or fakes the drop to avoid an opposing player, play shall be stopped and a last play face-off occurs.

601 - Abuse of Officials and Other Misconduct

What penalty is imposed on a player who collides with an Official and verbally abuses them for being in the way with no reference made to a previous decision?

A misconduct penalty. Rule Reference 601(c.2).

Since the player was not disputing a ruling, the verbal abuse falls under the misconduct rule.

605 - Broken Stick

A player has broken their stick, but is unaware of the fact that it is broken. What guidelines must be used when determining whether or not to assess a penalty?

A player is accountable for their actions, so the minor penalty shall be assessed if they participate in the play in any manner. Rule Reference 605(a).

Even though the player may not immediately be aware of the broken stick, there is no provision of the rule that allows them to legally participate in play.
In some instances, it may be appropriate for the on-ice officials to verbally alert the player their stick has broken. 

However, this must be done for the purpose of avoiding a penalty and done with equal diligence by all officials and to both teams.