Priority for flight deck crew is to deal with the emergency, and this will involve only essential communications with cabin crew, and even less so for the passengers.

In some cases, usually non-critical, a passenger announcement can be made time permitting.

ANCA is used by some organisations to prioritise the tasks:

A - Aviate, ie maintain control of the flight-path (speed, heading, altitude, power, and configuration (flaps, gear))
N - Navigate, ie safe heading, safe altitude, minimum alt, location of terrain and other hazards, on cleared route etc
C - Communicate, ie MayDay or Pan Pan radio calls, internal comms with other crew, allocation of responsibilities
A - Administrate, ie determine subsequent options/intentions, arrange ATC clearances and services required, contact operating HQ for ops and maint support

Once this is done, and often this means not until you are safely back on the ground with no ongoing issues (handling, fire), would you advise pax. The caveat is if the aircraft captain requires pax to be prepared for evacuation or other instructions.

From personal experience it can get very busy, very quickly, in the cockpit when things start going 'wrong'.