Well, just to address one part of your question, I wanted to say that YES!, the Universe is indeed contained inside a type of 4 dimensional "fabric".
It's often called the "space-time fabric".
Large objects are actually able to stretch, deform, and bend this 4 dimensional fabric, thereby creating an actual "valley", or "well", or "dip" in their region of space.
Interestingly, Einstein thought that this bending into valleys and dips, is essentially what creates our sense and perception of "gravity".
So while some seek to explain the force of gravity through particle physics, such as a "graviton" particle (that still hasn't been discovered yet), Einstein took a different approach and said that gravity was just simply a result of geometry.
So Einstein's view of gravity is also known as the "geometric" view. Geometry creates gravity, as objects fall into these valleys and dips!
By the way, this also means anti-gravity floating flying saucers, and space ships having artificial gravity deck-plating (of the type you often hear about in Science-Fiction), may not ever be possible, based upon currently known physics.
I mean how do you cancel out, and unwarp and unbend a vast region of the space-time fabric, being caused by an entire massive planet!?
But, while we don't have anything that can emit "anti-gravity" we can still of course counter the force generated by gravity valleys and dips, with powerful chemical rockets for now, or drones/helicopters that push air downward, etc...
As for the fabric of space-time, what exactly is it?
I don't think anyone quite knows what it is... for now.
But, shockingly we do know the Universe is constantly creating NEW space-time fabric every moment.
For example: picture yourself walking down a sidewalk... Sidewalks are usually divided into sections, with a crack between each section. So think of that as the sidewalk-grid.
Well, what is happening in the universe, is the equivalent of new sidwalk-sections mysteriously popping into existence!
Imagine you are walking down the sidewalk, and your home is 50 sidewalk sections away, and as you walk new sidewalk sections keep appearing, so that now your home is 100 sidewalk sections away. And as you try to traverse that, your home suddenly becomes 200 sidewalk sections away!
This is why we will never be able to reach the more distant galaxies, because new sections of universe's sidewalk keep popping into existence!
Those very distant galaxies appear to be accelerating away from us faster than the speed of light (because of all the "sidewalk-sections" that keep popping into existence between us and them).
It's not that the distant galaxy, and our own, are actually travelling faster than the speed of light, but rather that the Universe is simply adding more sections of fabric, between us and them.
ALSO... Fortunately there are NOT yet too many extra sections of the space-time being added between us, and the nearest galaxies.
So we will still be able to travel to the nearest galaxies in the future.
And of course, if we can figure out how to safely punch a hole through the space-time fabric, exit our Universe (moving into the realm of "hyperspace"), and then re-enter our universe at a more distant point, then we can travel vast distances by cheating in this way.