Yes, some directional control as we still have two functioning engines.

Airplanes can get uncontrollable during windshear.

To monitor the flight management and aircraft control actions of the Pilot Flying and carry out support duties such as communications and check-list reading.

Because usually the heated air bypasses the air filter, therefore it is possible for dust to enter the engine and so exposing the engine to unnecessary engine wear.

To varify the nose gear position (up or down).

To be the most efficient, aircraft descend at Vmd. Vmd increases with Weight, and therefore the rate of descent increases as well with weight.

TCAS works by sending interrogations to other aircraft's transponders.

The transponder will reply to the interrogation in a similar way it responds to radar. From the time difference between the interrogation and the reply, the distance to the other aircraft is calculated. The reply itself contains the altitude of the other aircraft.

The distance and the altitude difference with the other aircraft is tracked to identify a trend which may result in a TA or eventually a RA.

For a commerical aeroplane: During take off. At this point the aircraft has it it's maximum weight, and accelerating in the vertical plane requiring the highest ammount of lift to counteract the weight.

L = 1/2 * rho * Cl * A * V^2

A line across the surface of the earth that cuts all meridians at the same angle. i.e. a track of constant direction.

A straight line on a Mercator chart.