The fundamental nature of light is a bit hard to explain, and goes into areas where our intuitive understanding of the world simply no longer applies, so you're going to have to think of light in a couple different ways at the same time to try to grasp what's going on.
Light is an electromagnetic wave. That means that it's a disturbance of the electromagnetic field that travels at a characteristic speed. Like all waves, light has energy and momentum. Think of ocean waves breaking on a beach, tossing some light object back and forth.
However, while waves we're more familiar with, like ones in water, seem to carry their energy in a pretty continuous manner, when you look at light closely, you can see that its energy is actually carried in discreet packets called photons. Photons are very strange beasts that behave in ways that are hard to visualize. Sometimes they act like particles, and sometimes like a wave. They are both and neither at the same time.
At the scale of photons (which are really really small) the distinction between mass and energy gets a bit fuzzy. Photons have a rest mass of zero, which means that if you stopped a photon, it would have no mass at all. But photons always travel at the speed of light, c. Special relativity says that objects that move close to the speed of light appear to actually increase their mass, and a normal object with a positive rest mass would actually have infinite mass if it could be accelerated to c. The thing is that if you multiply infinity by zero, you can actually get a finite number. So photons do have an apparent mass, as strange as that sounds.
Because photons have an apparent mass, they are effected by gravity the same way as normal matter, and create gravity themselves. But because the apparent mass of photons is very small and they're moving very fast, normally the effect of gravity on photons is very slight.
General Relativity says that gravity isn't actually a force but a distortion of space that creates an illusionary force because of your frame of reference. Think about how you're pushed back in your seat when your car accelerates. It feels like there's a force pressing you back in the seat. But if you look at it from outside the car, you can see that actually the seat is pressing into you, accelerating you forward. Gravity works in a similar way - standing on the surface of the Earth, we perceive a force pushing us against the planet. But to an outside observer, you'd see that the mass of the Earth is actually bending space so that an object resting on the surface of the planet is actually being accelerated upwards by the surface of the planet, the same way the car seat is accelerating you forward. An object at "rest" in a gravitational field is actually an object that's in free fall. If you were in a sealed free falling room without an outside point of reference, you wouldn't be able to tell if you were in deep space far away from any gravity, or if you were near a planet falling toward the surface.
Because of space being distorted, anything moving near an object with mass will move along a bent path that follows the curvature of space. (Unless it's being accelerated by another force, like a rocket, for example.) This applies both to light and to normal matter. A satellite in orbit moves in a circular path because of the curvature of space, even though from the satellite's point of view it seems to be moving in a straight line. These curved "straight" lines are called geodesics, and represent the shortest distance between two points while conforming to the curvature of space. This is like how if you look at a map with the course of airplanes, it will look like the planes are curving way out of their way toward the poles, but if you look at a globe, and stretch a string between two points, you'll see that the planes are actually going in a straight line.
As for light moving at different speeds, that's because of the way light interacts with matter. Photons (and all other particles with a zero rest mass) *always* move at exactly c. When light travels through matter, like air, water, or glass, the light appears to move more slowly because the photons hit the atoms in the material and are absorbed by them. That energizes the atoms, and they then emit another photon with the same energy. It's like how a train moving along a line with lots of stations will have a lower average speed then an express train that doesn't stop, even though both trains move at the same speed in between stations.
As for "breaking" light, I'm not entirely sure what you mean, but light, like everything else follows Newton's first law of motion - an object will travel in a straight line at a constant speed unless acted on by an outside force. If an astronaut in deep space throws a pebble into the void, that pebble will keep going forever unless it hits something. Light is the same way - it just keeps going. Light is not the only thing that travels vast distances across the universe - high energy cosmic rays are believed to come from very distant supernovae. We tend to use light to study distant objects because how much it interacts with matter just right. It doesn't interact too much, so it can travel vast distances without being changed too much. But it also interacts enough that we can capture them and study them. Some things interact too much, like cosmic rays, that are mostly charged particles that get tossed every which way by electromagnetic fields, so we can't tell where they come from. And some things interact too little, like neutrinos, that pass right through ordinary matter so easily we can barely tell they're there.
PS Light does interfere with itself the same way sound or water waves do. We don't normally see it in day to day life because ordinary light is incoherent - it's made up of waves that are all different frequencies and oriented in all different directions, so the interferance patterns are either mostly too small to see, or are washed out by all the rest of the light around. Coherent light, like that produced by a laser, is all the same wavelength and all arranged the same way, so you can see interference effects pretty easily with that. Interference between laser beams is actually often used to make very fine measurements in physics.
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