Are sudden turns and descents a standard emergency procedure?
There are no emergency procedures I'm aware of that requires a pilot to turn left 90 degrees and then turn right 360 degrees.

There is a procedure for situations requiring rapid descent for things like medical emergencies and fires.  They consist of a 45 degree banked, full-flap, power-idle descent flown at maximum flap extension speed.  So it is a spiraling-turn descent.

Also, the Cessna 172N checklist instructs the pilot to slip in the opposite direction from a wing fire to keep the flames blown in an outboard direction.