Thorough knowledge of mathematics is necessary, and expect one purely mathematical question in the NSEA Exam.
All topics of physics mentioned for NSEA are important with thorough and complete knowledge. Just because NSEA is an astronomy Olympiad doesn't mean it will ask questions only related to astronomy.
The questions in NSEA are highly calculation based. Almost 10 questions will involve just mathematical calculations.
Probability is important.
The next most important topic: Gravitation. Expect all kinds of questions from here.
Optics can also be expected since telescopes and optical instruments are important to astronomy. Mechanics (Newton's laws, kinematics, the centre of mass, work energy power, collisions, rigid body dynamics, relativity in order of the importance), Thermodynamics, Heat transfer (especially the topic radiation), Waves and Electromagnetism.
Rigid body dynamics, it seems, does not have that much weightage.
The questions are not difficult but are time-consuming with lengthy calculations. Be prepared.
Calculations are what make NSEA different from NSEP. Hardly any question from pure astronomy is asked.