About black holes, is it possible there's not actually a singularity - no infinitely dense point - to black holes? From my understanding of relativity and time dilation, time gets slower and slower as the gravity's escape velocity grows closer and closer to c, meaning that nothing can pass through the event horizon by themselves.
Yes, it's totally possible (perhaps even expected) that in reality, black hole singularities are not actually infinitely small. That everything is compressed to singularity is a prediction of general relativity. Once the collapse has brought the matter within its own Schwarzschild radius, it cannot be supported by any pressure forces, and the only direction it can possibly move is further inward. It is thought that some future theory of quantum gravity will lead to different predictions about the nature of the singularity, though this will not change the behavior of the rest of the black hole or its horizon.
The bit about time dilation's role in the collapse is a common confusion -- even the relativists first studying the collapse had difficulty with this. The way it works is that, f
or the observer outside the black hole, time does come to a halt at the event horizon. So according to them, the black hole actually has no interior! All the matter is "smushed" into very thin shells that get closer and closer to the horizon. (They also vanish from view, because the light is also being redshifted to blackness, which happens
very quickly.)
But for the frame of reference of the material collapsing to form the black hole, or for someone falling into the black hole sometime later,
time does not halt at the horizon. The collapse proceeds basically as a free-fall all the way to singularity, and in a very short time according to clocks in this in-falling frame. So if you jump into a black hole you
do pass through the horizon without any hang-up, even though to someone far away they never see you reach the horizon.
Also, inside of the event horizon, would time travel backwards? Because I believe that time travel to the past is extremely paradoxical and therefore impossible, I'm starting to doubt that even event horizons actually exist.
Not quite. What happens is that time and one of the spatial directions switch roles. The inward direction acts like the direction of the future, so once inside the horizon you are forced to move further inward. To move outward would be equivalent to travelling into the past, which as you say, is quite forbidden!
A very good way to think about it is as if you are fish about to go over a waterfall. At some point, the current flows faster than you can swim, so even if you try swimming upstream, you're still going farther down. This point where you can no longer possibly escape is location of the event horizon, and the singularity is like the sharp rocks at the bottom.
Now, I am quite possibly wrong, since my understanding of Einsteinian relativity and quantum mechanics is small. Sadly, no high school that I know of offers those courses. Although if my understanding is correct, there should be this interesting result: black holes have holes inside. They're bubbles!
Yeah, I don't know of any High School that would teach these subjects, but if you go through a physics program at college or university you'll get some much deeper knowledge about them. There is also lots of material available freely online.