Once an object or particle passes the event horizon, will it ever reach the center of the blackhole. I ask this from my elementary understand of relativity. This is my understanding: if an object passes the event horizon, essentially, even if it were moving at the speed of light, it couldn't escape. In my mind, the gravitational pull inside the event horizon pulls particles at a speed greater than the speed of light. As time reaches the speed of light it slows down, which means the object exists at time zero. So will it ever reach the center of the blackhole?
Well, it depends on the theory, but more popularly it does. When it comes to particles in a black hole obviously they cannot be observed. A black hole doesn't really "pull" particles in, it just has a very strong gravitational pull, so much that light is not moving fast enough to escape the acceleration towards the singularity. But essentially, according to the more widely popular black hole theories all particles go into the singularity which is an infinitely tiny point, so it does reach the "center" if it didn't, it would not work because time inside a black hole flows. Things happen inside that it emits radiation, and it would not be able to gain mass if everything froze inside of it, there would be no singularity. Here is an article that will tell you about some of Hawkings theories if you like http://www.hawking.org.uk/into-a-black-hole.html
First I don't think any object, even though it is being pulled towards a black hole, can ever exceed the speed of light. As the object accelerates towards the black hole, its inertia continues to increase, F=ma, which makes the acceleration decrease, eventually will never reach the speed of light.
By the "center of the black hole", you mean the singularity.
As time reaches the speed of light it slows down, which means the object exists at time zero.
This will only happen to the observer, put in another way, this is the frame of the observer. Its time will seem to be slower than ours.
But to the object itself, it will never notice anything different, the time will still go, the physical effects will remain the same.
The object will never reach the singularity as a whole because by the time it gets there, the huge tidal force generated by the black hole will tear the object into atoms before it even reaches the center of the black hole.