Explanation:

First is incorrect. Nataraja is concerned with Atibhanga not Tribhanga.

Bhangas are of 4 kinds:

1. Abhanga (slight flexion)
2. Samabhanga (equipose)
3. Atibhanga (excessive flexion)
4. Tribhanga (three flexions)

1. Abhanga (slight flexion)
The Abhanga pose is shown in standing gracefully with weight of the body placed on one leg. It indicates meditation, repose and serenity.
2. Samabhanga (equipose)
Samabhanga is the gracious pose of seated or standing figures in equipose.
3. Atibhanga (excessive flexion)
Atibhanga is concerned with the dramatic dance forms called Tandava i.e., the Nataraja poses of the dancing Shiva, the delighted dance of Krishna and others.
4.Tribhanga (three flexions)
Tribhanga posture is the thrice-bent figure in which the head is inclined to one side, the upper body is bent in the opposite direction and part of the body below the waist takes again the reverse direction. The Tribhanga actions are dramatic energetic muscle actions.

Third is correct. The dance-gesture, mudra of left lower hand is called Dola hasta, a munificent hand. This gesture indicates that benefits of living are bestowed as well as the benefit of dying, i.e. moksha, final liberation, from the cycle of birth and death, if the seeker is a correct knower of truth.
Fourth is correct. The lower right hand is called abhaya hasta, the blessing hand, symboling safe existence. The creation shall exist till its sojourn is complete, which is blessed with this hand.