It's a bit unclear what you're asking, but I'll run with the part: "What do we get as observers from being in 2D rather than 1D?" I've also italicized a few things which answer the sub-questions in your question.
TL;DR You get a lot of complexity with each added dimension, and that might seem nice for humans. But lots of cool things happen in just a few dimensions. For example, sound is a two dimensional phenomenon. Maybe we wouldn't be able to process it (brains are at least three dimensional), but music could exist nonetheless and I think there's something to be said for that.
Let's start with Dimension 1:
It's easiest to think of this as a line. We don't get much with just one dimension, and the world is pretty boring. We can think of distance between points on that line, and we can think of whether or not points are on top of each other (distance of 0). With that, we can say "I'm further away from point A than point B, and if I was closer to point A I would be further from point B."
There's another way of thinking of one spatial dimension. Imagine a single point, which we assign a "direction." What does that mean? Well... It can point any "direction" we want, from 0 to 360 degrees. That's no different than assigning points on a number line. The "angle", as we call it, is the dimension. And we can talk about how two angles are different, or are the same. In fact, we usually say that angle 0 and angle 360 are identical, which gives some weird properties. "I'm further away from angle A than angle B, but if I rotate closer to angle A I also get closer to angle B in some way." Funky! But this lets us talk about rotation in as few as one dimension.
But obviously, there still isn't that much going on in one spatial dimension.
It's easiest to think of this as a plane, like a map. There is an up/down and a left/right. Or you can think of it as latitude and longitude, which is sorta like a map except all the edges are connected. Or you can think of it as polar coordinates, like a radar readout.
What distinguishes two dimensions is that two points can be in the same place in one dimension but different places in the other. We can do a lot more with two dimensions. Distance becomes much harder to define. Interesting shapes emerge. The world as you would see it through one eye, and hear it through one ear, begins to exist. Flat drawings can exist, although I'm not exactly sure how one could perceive them (if I recall correctly, Flatland really gets at this).
Sidebar on sound, because I think it's fascinating:
Against your eardrum is a wall of air (a 2D plane), which moves in a direction perpendicular to the plane (a 3rd dimension), over a period of time (a 4th dimension) to make you hear noise. However, sound is really a two-dimensional phenomenon! A microphone converts our many-dimensional sound into a two-dimensional signal, and a speaker converts the signal back into four-dimensional sound. The signal in the middle is still "sound" in a pure sense--it's just that humans aren't designed to hear in two dimensions so we need to it be converted up. So when it comes to noise, there is no benefit to 3 or 4 dimensions except that humans are designed to work in that number.
Lets get back to...
This is where things start to get really real. Each dimension, left/right, up/down, in/out, is independent of the others. The world, in a snapshot, exists. Sculptures can exist. You, geometrically speaking, exist. Textures exist. There are a whole variety of three-dimensional spaces, which can take on strange shapes and properties. But even in our own pretty much Euclidean space, three dimensions lets us easily perceive the vast breadth of two-dimensional objects with our eyes and our ears. A two dimensional drawing could exist in two dimensions, but to actually see it, you need three.
But we're still kinda missing something...
Time (usually). This not a spatial dimension, but it's important. It gives us before and after, movement, etc. It gets pretty funky once you look at special or general relativity, but that seems out of the scope of this question. What matters most is that it animates the other spatial dimensions. But it doesn't have to be the fourth dimension. You could just as well have a world with only two dimensions: a line, and time. Or three dimensions: Cartesian space, and time, kind of like Flatland.
What I hope to show by this is that with each added dimension, we get a slightly more complex world which we perceive to be beneficial to humans purely because of the way humans perceive the world.