How does light fill the entire universe? Light is a particle and a particle is discrete. So say light is emitted from a star 7 billion years far, how is it possible that this light particle emitting from a star fills every point in the universe anx it reaches us?
And when light behaves as a wave then yes that explains the interference but what kind of wave is this that reaches every point in universe?
 A: The first part of the answer is that a star produces a lot of photons.
Let's take our favorite friendly neighborhood star as an example.  The Sun's luminosity is about $3.83 
\times 10^{26}$ W.  If we pretend for a moment that all of this light is composed of photons of wavelength 550 nm (definitely not true, but it will give us the right order of magnitude), then the Sun produces about
$$\frac{3.83 \times 10^{26} \text{ W}}{hc/\text{550 nm}} = 10^{45} \text{ photons/second}$$
This is such an enormous number that the density of photons remains significant even very far away from a star.  For example, photons from a sunlike star on the other side of the Milky Way galaxy, about 100,000 light years away, would strike Earth at a rate of about 100 photons per second per square meter.  That's why it is possible to detect distant stars with a telescope.
More conceptually, light is (as you noted) both a particle and a wave.  As such, it is possible to write a quantum mechanical wave function describing the light that is emitted from a star.  The validity of the wave function description doesn't mean that photons do not also exist!  Unlike macroscopic objects, however, individual photons are quantum particles that do not have a precise, well-defined location.  Instead, there is a probability density (described by the wave function) that a photon will be detected at a given location in space at a given time.
As we go farther and farther from the star, these probabilities become lower and lower.  Eventually, very far away from the star, it becomes unlikely that a photon will be detected in any particular region of space at all.  At this point, the wave function takes on very small values but remains nonzero.  So one can reasonably say that the light wave spreads throughout the visible universe, but it's very unlikely that the light will have any measurable effect on a distant human eye or telescope.
A: That's actually a great question.  The way I would think of it is, the way the EM field propagates at every point is by oscillating its value, which then affects the values of the field at the points in its immediate surroundings, and then those points do likewise, so on and so forth. So there are no "gaps." Hyugens Principal explores this.
I've also heard it said that discrete photon behavior only manifests when there is an interaction with another particle. But I'm not a QM expert so can't really speak to that.
A: When studying physics one has to keep in mind clearly the framework on which the theory for the observations is valid, and not mix up concepts of different theories.

Light is a particle and a particle is discrete.

Light is described by the classical electrodynamics of Maxwell equations, and it is not a particle, it is a wave, described by wave differential equations

So say light is emitted from a star 7 billion years far, how is it possible that this light particle emitting from a star fills every point in the universe and it reaches us?

Light is not a particle, it follows the rays of classical solutions and from a star radiates all around , moves with velocity c and reaches us after a calculable classically time if it does not fall on stars etc on the way.

And when light behaves as a wave then yes that explains the interference but what kind of wave is this that reaches every point in universe?

Light is a wave can only be modeled with the wave equations of Maxwell
Particles are in the frame of quantum mechanics, and the classical light wave is built up by an enormous number of photons, elementary particles of zero mass energy $hν$ where $ν$ is the frequency of the classical wave built up by a huge number of photons,in a quantum mechanical way that can only be understood with quantum field theory (this blog entry for example treats this ).
Our understanding of nature has moved from philosophy and hand waving to modeling phenomena with mathematics, and it needs serious study to really understand phenomena.
This single photon at a time double slit experiment may show you the complexity.


Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

The photons leave a footprint of a particle, their accumulation shows the wave nature, which can be seen as  a probability distribution for detecting a photon at a specific (x,y) on the screen. The wave nature of photons is in the probability distribution, not in space.
