How does warped space actually look (visually)? Recently, I was reading about space warping due to extreme gravity and at speeds approaching c, but in books, they always show space in 2D and depth to show space distortion. I was wondering how exactly warped space look in actual? 
 A: As you travel through the warped spacetime, you would not notice much difference. This is because any spacetime regions you are likely to ever encounter look exactly the same as flat spacetime locally. This is great news for us because it means we'd always be able to assume that propelling ourselves forward will actually make us go forward and not to the side or something weird like that.
As a distant observer, we can actually see what warped space looks like. A phenomenon called gravitational lensing allows us to see the warping of spacetime as light passes by objects of large mass. Take a look at the picture below. That ring around the star is the light from a galaxy behind the star that has passed through warped spacetime.

Practised observers can actually see a few more examples of lensing in that picture (I can see 5 others, but I'm not an astronomer. How many do other people see?), but you get the idea. Pretty cool, eh?
Understandably, you may feel that this visualization does not give you an intuitive understanding about how things should behave in warped spacetime. That is why you often see the 2D simplification; it's easier to get the point across. But if you want a visual image of how gravity actually warps/curves spacetime, you'll find nothing better (at least, nothing I can think of) than a nice picture of an Einstein ring, like the one above.
Picture taken from Wikipedia
A: When we visualize a Riemannian manifold from outside, abstractly, as a part of ordinary space but with a different metric, like in the disk model of the hyperbolic plane, we get very nice images, but it looks very different from how it would look to a creature living inside of it.

When you are inside, it doesn't look all that distorted, because you, and light rays, etc, all get warped in the same way. While walking toward the boundary in the hyperbolic disk model, you would just get smaller with every step. You would notice some things however, like parallel lines that move away from each other, triangles whose angles don't add up to $\pi$, etc.
The following is an image from inside hyperbolic space, made long ago by the geometry center, showing a tessellation of space with regular dodecahedra, which obviously is impossible in Euclidean space. 

As Johannes mentioned in a comment, the movie Interstellar has some pretty accurate and high quality graphics of gravitationally warped space, like this image of a black hole with its accretion disk.

Note that the disk essentially lies in a plane, light from the central part cannot escape, but light escaping initially away from us may bend into our direction, so we see the disk essentially everywhere around the black hole. However, you don't directly see that you are in curved space, you just see that light is bent by gravity, and qualitatively it doesn't look different from how it would look in flat space in which light was bent by gravity.
A: Space-time is founded on the idea that mass/energy do not change, but that space, that which contains all things, changes.  Consequently the concept of time is reflective of this change in space.
In other words, the speed of C is constant, and consequently so is mass.  The only thing that is relative is the changing of space and our idea of time.
"Seeing" this is as easy as looking around your home or office.  The very reality of change is space-time at work.
