Firstly, thinking of gravity as a force is a fairly decent way of understanding it. The model breaks down in some situations, but is not bad most of the time. Gravity as a force is a helpful lie, which is why we teach it.

The GR way of looking at gravity is as curvature in spacetime. Essentially the presence of energy/mass squishes space and time together around it, meaning that there is "more space per space" close to a massive object, and "less time per time" (time passes slower).

One way of thinking about falling is that this effect twists an object's time direction a bit into its space directions. The object falling is sitting where it is doing its normal thing, staying still and going forwards through time at 1 second per second. But from an outside perspective it is going forward through time at a bit less than 1 second per second, and is also moving downwards a bit, because its "forward through time" direction is an outsider's "forward through time and a bit down" direction [disclaimer; this isn't quite how the maths works, but is a helpful analogy].

A more massive object has more of a twisting effect on spacetime, so this is a bigger deal for more massive objects. It's also a bigger deal closer to massive objects than further away; acceleration due to gravity is about 9.81 metres per second-squared near the surface of Earth, but it drops the higher up you get. It is about 90% of that on the International Space Station, for example.

I'm not entirely sure what you are saying about accelerations of objects. It is possible to mimic the effect of gravity by being in an accelerating reference frame - that is kind of what a g-force is (which is not due to gravity, and not a force - great naming there, guys!). But in that case we're simulating the effects of gravity - depending on the acceleration we can vary the fake-gravity's strength.

Firstly, 9.81 feet per second is a speed not an acceleration. Acceleration due to gravity is 9.81 metres per second per second. I just dropped out of a University module on relativity. What we experience as gravity is a consequence of how mass-energy curves spacetime. Objects tend to move along paths of least effort, essentially looking for the shortest path through curved space.

More massive objects curve spacetime more than less massive objects, just as a massive ball on a rubber mat curves the rubber mat more than a lightweight ball.

In VERY short: A more massive object bends space-time more. The 4d space-time is shorter between more massive/greater curved space. The shortest distance in 4d is always travelled. The distance between them passes faster. We perceive this as moving faster in 3d space. Higher acceleration.

as far as I know there are a few things wrong here:

1. we don't fall towards earth at 9.81 fps, the earth's gravitational force accelerates us at 9.81 m/s², that's why we even feel the force (think of sitting in a car, you aren't able to feel how fast you are going, but when you accelerate you are pressed into your seat).
2. gravity actually is a force, it's one of the 4(?) natural forces of which some can be explained better and some worse. The other 3 forces are the weak force, the strong force, and the electromagnetic force
3. I think you are referencing Einstein's thoughts about relativity. He said something like acceleration through space and the gravitational force work in the same way, if you are in a closed room (say an elevator), you can't differentiate if there is a gravitational force pulling you down, or if the elevator is going up and pressing against you.

You're right that you can think of gravity as something that isn't a force, but it works differently than what you describe in your post.

Essentially, an object with no (non-gravity) forces on it will trace out a straight line through space-time. This is basically inertia: an object won't change speed unless some force acts on it, and if you chart out the path an object moving at a constant speed traces, it follows a straight line. Technically, it's called a "geodesic," not a straight line, but that's essentially the general concept that includes "straight lines."

Gravity happen because geodesics tend to get closer to massive objects. This seems strange; for instance, if you were on a spaceship moving next to the earth at exactly the same speed in exactly the same direction, the paths you and the earth are taking would be parallel. There'd be no significant forces affecting your ship and the earth, so you'd expect those forces to stay parallel since you're moving in a straight line, but your spaceship would get closer and closer to the earth until you eventually crash. This is because spacetime isn't "flat," and geometry in curved spaces behaves differently than geometry in flat ones. As an example, if you take a globe and draw two lines next to each other, perpendicular to the equator, those lines look parallel. But if you continue to draw the lines straight (technically, drawing geodesics on a sphere), they would intersect at the north and south poles. That's because the surface of a globe is curved in a way that "parallel" lines eventually cross.

Something similar happens with spacetime. Mass (and energy) itself causes spacetime to curve. It doesn't seem to curve into anything, in the same way that a globe curves in 3d space, it just sort of intrinsically is curved. We also don't really know why energy curves space, beyond "it just does." But it does curve spacetime, and it curves it in such a way that the geodesics that other objects follow tend to get closer to it over time. Heavier things curve spacetime more, which makes geodesics get closer in a more pronounced way, which makes objects fall faster.

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Bigger objects bend space more.

Place a marble on the trampoline. When you stand on the trampoline, you the marble will roll towards you. The heavier you are, the faster the marble will roll towards you.

The more you can stretch the trampoline, the more you affect other objects on it.

Get too heavy, and you’ll poke through, like a black hole.

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That's not how gravity works, as far as I know. Gravity is, indeed, a force, that becomes stronger proportionally to the mass and distance of an object. Jupiter has more mass than Earth, so it has an stronger gravitational force, so it pulls objects towards it with more strength.