In regard to speed, the speed of light is actually the speed of causality, which is the absolute limit at which one event can influence another. It is an absolute speed limit. Light can travel at this speed limit because it is a massless particle/wave. Anything with mass would need to have infinite energy to travel at the speed of light because the faster something is traveling, the more energy it takes to accelerate it further.

Inside the event horizon, these same rules apply because it is still space and time inside the event horizon. Even light that is traveling at the speed limit cannot escape. You just can’t go fast enough to escape once you are inside the event horizon, because the speed limit of the universe prevents you from going fast enough to escape. Basically you would be on your way to being spaghetti-fied as you approach the black hole, or maybe not. There is a whole lot we don’t know about the inside of black holes, so who knows what could happen in there. There are theories that say that super massive black holes could have different effects on things, but I only know of them and not how to explain them.

Outside of the event horizon, you can technically escape by accelerating away. But it would require so much energy that you wouldn’t want to cut it close, I would think.

Gravity does bend space and that does cause light to curve along with space. If there’s enough mass, it can bend space enough to essentially make a lens that can magnify light coming from behind. A black hole can bend space so much you can see the opposite side of its accretion disk above and below the event horizon.

If you’re interested, I watch a lot of Antov Petrov, Cool Worlds, Dr. Becky, and PBS Space Time on YouTube. That’s where I have learned most of this stuff. PBS Space Time can be a bit hardcore sometimes, but they have tons of information.