Rule 304 - Protective Equipment

What action should the referee take when the goalkeeper loses one of their gloves during play?

Keeping safety as the primary consideration, the referee should stop play whenever the goalkeeper loses a glove and is in a vulnerable position UNLESS there is an imminent scoring opportunity in which play should be allowed to continue until the imminent scoring opportunity has passed.
Rule References 304(a and e).

If the Referee judges the goalkeeper has deliberately removed any equipment during play they should assess the offending goalkeeper a ‘Delay of Game’ minor penalty.

Rule 401 - Penalties

An Official blows the whistle to stop play. The players around the puck do not hear the whistle and the play continues. During this time, a player commits an infraction that calls for a minor penalty. Should the Referee assess the penalty even though play was supposed to have stopped prior
to the infraction?

Yes. Rule Reference 401(a Note 1).

The penalty must be assessed even though the play has technically ended. Penalties that occur during stoppages of play must be called as if they actually occurred during normal playing time

 Rule 402 - Minor Penalties

A player is assessed a minor penalty and then their team is assessed a bench minor penalty during the same stoppage of play. The player’s Coach requests that the player also serve the bench minor penalty? Should the Referee permit this?

No. Rule Reference 402(b).

Because the bench minor penalty is assessed to the team and not to an individual player, the Coach must designate a non-penalized player who was on the ice at the time of the infraction to serve the bench minor penalty. The team will then play short-handed by two players for two minutes, unless a goal is scored that would terminate a minor penalty