What is gravity and what causes the existence of gravity? Gravity in some cases has been described as a fold in space time, as there seems to be a distortion in the continuum, and while analogies convey that objects just seems to fall into this distortion hence what I am asking is what is gravity exactly and how is this force existing in the universe, i.e. gravitational pull of the planets?
 A: If you read about the history of physics, how various theories, i.e. mathematical models of nature have been developed, you will know about the apple and Newton developing the first model truly describing mathematically the planetary system and being predictive of the observed  motions of matter, falling apples as an example. This theory has axiomatic definitions, called laws , and force is a concept that is used both for gravitational mechanics and kinematics.
Further progress in theories of physics lead to the equations of Maxwell and the explanation of what was observational laws, and the prediction of electromagnetic waves.
Electromagnetism lead Einstein to first posit  the special theory of relativity, imposing Lorenz transformation on massive bodies, and that lead to his forming General Relativity , as distortions of space.
The important thing to remember is that the consecutive theories are nested. Special relativity at low velocities becomes Galilean relativity. General Relativity at the limits of small masses and energy becomes Newtonian gravity. 
There is consistency and continuity , because finally one describes nature with the theories of physics, so the successful theories , i.e. validated by observations and experiments in one part of phase space must necessarily be included at the limits of the later and better theories.
So the real answer to:

what is gravity and what causes the existence of gravity?

Gravity is a force that is needed to describe observations and data at low energies and small masses. Force is an axiomatic definition in the laws of mechanics.
A: In general relativity, matter (or more correctly the energy-momentum tensor) causes spacetime to have curvature. If no external forces act on a test particle then it will follow the straightest possible path through spacetime, called a geodesic. This may be a curved path through three dimensional space but it is a geodesic nonetheless. The gravitational force is a consequence of this. Gravity is completely a geometric property of spacetime.
A: Gravity is a conservative force which exists between any two objects in the universe due to their mutual attraction. The force exists due to attraction between any two masses. For example the stability of universe is because of this force among planets . It is so beautiful that gravity although exists between sun and earth as well as earth and any other planet is solar system but because of variation of size of planets and distance between planets the earth ir any other planet moves around sun instead of revolving around each other
The concept of introduction of gravitational waves shows how masses which move at speed of light can transport energy as gravitational radiation
A: Same as with other fundamental forces, there is interaction particles, i.e. gravitons for gravity same as photons for electromagnetic force. Interaction particles are mostly virtual all the time. 
When two masses just stand still, there is virtual gravitons jumping back and forth between those with lightspeed, creating the force which pulls those masses together. When one mass is moved, other mass does not know that before graviton is reaching through the space.
LIGO/Virgo is essentially giant detector of gravitons with positive energy.
Physics have different mathematical representations. Spacetime with curvature (nonmaterial field) is one way to represent the Einstein's General Relativity, mostly described by Einstein himself. There were other approaches found later. And it was shown that different mathematical descriptions are making same General Relativity, i.e. they create same solutions.
One example of different representation is with material gravitational field - Logunov's theory of gravitation (RTG) https://arxiv.org/abs/gr-qc/0210005
