  This doctoral thesis is organized into seven chapters. The first chapter
introduces readers to the formation of black holes and naked singularities as
an end state of continuous gravitational collapse. The physical and geometrical
properties of the Schwarzschild black hole, JMN-1 naked singularity, and JNW
naked singularity are summarised. The motivation and objectives to be derived
are based on the literature reviews. The second chapter deals with the shadows
of the mentioned compact objects. The equations of motion are explicitly
calculated for general spherically symmetric and static spacetimes using the
ray-tracing formalism and the null geodesics. The third chapter focuses on the
construction of rotating naked singularity using the NJA. The NJA is used
without complexification method and obtain rotating JNW naked singularity
spacetime. The general formalism of the shadow shape is derived for rotating
spacetime and obtain the shadow shapes for the rotating JNW, Kerr and deformed
Kerr spacetimes. In the fourth chapter, the precession of timelike-bound orbits
is investigated in the Schwarzschild, JMN-1, and JNW spacetimes. The fully
relativistic orbit equations are derived for the provided models. The
approximate solutions of the orbit equations are used to characterize the
nature of orbital precession. The next chapter is on the precession of timelike
bound orbits in the rotating Kerr and JNW spacetimes. The sixth chapter deals
with the relativistic orbits of S-stars and discusses the orbital parameters of
the real and apparent orbits. Astrometric data of the S2 star has been adopted
from the available literature and use numerical techniques to study the
relativistic orbits of the S2 star in the presence of a scalar field. The final
chapter aims at summarising the results followed by some futuristic scopes that
probe the nature of Sgr A* with a possible black hole mimicker.
