The mass of an object increases closer to the speed of light because you can not pass the speed of light and the more energy you pump in, it will be converted to mass as the equation predicts "E=MC2" and this is the cause for time dilation, because gravity is inversely proportional to time.
1. I believe the easiest way to describe a black hole, to start off, is an object that is not an object. There are multiple theories about how black holes affect space-time, which all lead back to a bend in space time itself. Think of a piece of paper being stretched with nothing underneath it, with a heavy ball in the middle, and think of how that bends. That's the general consensus of how a black hole affects space-time, it simply bends it. The reason behind this theory, links to how a black hole is formed. A black hole is formed when a massive object exceeds it's own weight by diameter, by at least 500 times the weight of it's core. The collapse is so great, it collapses in on itself faster than the speed of light, causing a mass in the center to become so infinitely dense, that not even light can escape from the gravitational field of the event horizon. The event horizon is the point of no return where an object can not escape a black holes gravity. Because not even light can escape from a black hole, being a weightless wave source, it is generally accepted no object can escape a black holes gravity.
Basically, a black hole is an object so dense that there is no physical object within it. Because of the gravity involved, it creates a gravitational singularity, in which the gravity is measured to be infinite.
2. Light is not a physical particle, but a form of radiation. Charged particles can not reach the speed of light, as they would need an infinite amount of energy to do so (at least with present day technology).
3. The speed of light is not necessarily constant. It is only believed to be constant in a vacuum. The reason behind this, is that all experiments utilizing general relativity in a vacuum for other means came out to be accurate with the idea of light having a universal constant in a vacuum. However, this also can be changed with future research. Honestly, it all depends on whether a photon has mass or not, of which we are not completely certain. If it does, the speed of light would change according to multiple contingencies, but we don't have to get into that at the moment.