I am confused regarding how to bend my elbows while going down in a push-up. If we are observing a person doing a correct push up from the top i.e that his back is visible to us, will his/her body create a shape of 'T' while going down in a push-up or will it be a 'VIV' with both the arms forming the 'V's?
Welcome to Physical Fitness.SE!
Like with bench pressing, elbow position is important for push ups. The elbow position determines the shoulders' movement and which muscles contribute to the exercise. When you flare out your elbows, or look like a "T", the chest gets less of a workout. This is bad since pushups are primarily for the chest. This flaring also puts the shoulder joints in a risky position and the likelihood of injury is greatly increased (I learned this one the hard way and extremely do not recommend).
The ideal angle is to have the elbows about 45 degrees from the torso. This lays a solid foundation to push from and the majority of the power comes from the pecs. Bringing your elbows closer to the torso (so practically parallel with the body) will shift the focus more onto the triceps and you can work out other muscles safely.
Check out Athlean-X's video on good pushup form where he expands on proper techniques and, if I recall correctly, alternatives to the standard pushup.