It's not the speed of light you need to be so concerned about but time. Time always progresses for you at the same rate. Now the time elapsed between various local reference frames is variable compared to yours (and indeed the speed of light is as well) but for everyone everywhere they experience their own time at the rate of , one second per second, one cannot even imagine experiencing their own time as anything other than that, the idea is meaningless.

Light is similar, light always propagates through space at the "speed of time" which is 300,000,000 meters per second. This isn't the speed of light, this is the speed of causality, light just happens to propagate at the maximum speed, along with gravity, which can be understood as a kind of flow in space itself. Much like ripples in a pond. Or how sound travels in air. There's a maximum speed that phenomenon can travel through a medium, and that medium of the universe, the aether, isn't a medium in the traditional sense but space itself. And the speed at which it propagates is the speed of time. We can't go beyond this as to do so would mean going outside of the universe. Which is in and of itself a notion that we cannot fathom.

So in air, weird stuff happens when we start to travel faster than sound. But since matter isn't propagating through air but space, it's easy to go faster than that. But with the speed of light we are going at the propagation speed of energy, we can't go faster than that anymore than we can travel slower than zero. The idea with a warp drive is essentially to somehow move the space between places. Think kinda like how you could be in a wind tunnel where the airspeed is going at the speed of sound but so long as you are moving along with it at the same speed, the air will appear to be at rest to you. Similar concept. Except we are dealing with something, in this case space/time, which we don't fully understand, nor do we have the ability to manipulate it in that way.

I find one of the easiest ways to visualize this is the light clock idea. You have two mirrors on a spaceship and it takes the light a second to travel between them. As this spaceship accelerates the light from the light clock has to travel farther in terms of absolute distance in the perspective of a distant observer, and they'll begin to see that "time" on the spaceship is moving slower because of this effect, while on the spaceship itself they'd not notice a difference locally for them, but the outside universe would appear contracted, in both elapsed time and space itself, to make up for the fact that the light has to cover a longer and longer distance each second that elapses as the ship goes faster.

Once the ship reaches the speed of light it would appear frozen in time to the distant observer, and therefore unable to accelerate further. Of course reaching this point takes an infinite amount of time itself as any ship approaching the speed of light will appear more and more massive and will accelerate slower and slower as a result to the distant observer. For the people on the ship they just continue to accelerate at the constant rate forever as the universe outside appears more and more contracted in time and space towards infinity.

I think the infinities are what get people with these ideas. The very idea of simply adding more forever, itself being impossible, is hard for the human mind to grasp due to the boundless nature of the numbers involved. It's very much impossible for someone to even achieve the speed of light because of this as it would take an infinite amount of energy to do so. And an infinite amount of anything is of course impossible as we can always simply add more. As such I do say that the speed of light itself is indeed infinite. No matter how fast you go it will always be faster. Even though we can clearly measure the speed at which things happen, including light. That's the speed of causality more than anything. Which despite the name relativity is the constant upon which the entire theory relies.

This is one of the reasons why I suspect that the idea of black holes aren't exactly as our current mainstream scientific theories describe. They certainly seem to exist but relativity does mean that from our perspective it would take an infinite amount of time for one to form. So the ones we see I suspect are stars still in the process of collapsing into black holes but collapsing slower and slower as time goes on but never quite reaching an event horizon or singularity.

Since an object at rest falling into a black hole would reach the speed of light when it hits the event horizon, and since we know that would require an infinite amount of energy, is it not impossible?

I very much doubt that a black hole consists of such a simple idea of an event horizon and singularity, I suspect they are more like an extremely complex lattice of extremely dense matter right at the edge of forming an event horizon though from perspective of the distance observer.

From the perspective of the black hole itself, as we as the perspective of anything falling in, I suspect they are extremely short term objects. If hawking radiation is real then they'd evaporate out from under you before you hit them and you'd likely get fried by the now extremely blue shifted radiation coming at you.

Of course this is the problem with lights speed thought experiments in general. If you actually used some kind of infinite acceleration engine in real life you'd quickly get pummeled by now relativistic space dust and blue shifted to hellish levels of radiation that it would just utterly destroy any and all matter achieving the insane relativistic speeds required for the kind of time dilation necessary to traverse galaxies.