Space-time can be curved? why can't we see it

Because of the scale of size, and we can see dimension of time only at the rate one nanosecond per nanosecond, or smaller. We can't see that the Earth is spherical while we are on the surface of the Earth, because of the spatial scale of size in comparison with out own spatial scale of size. How far away a person's horizon is depends on their elevation. If you've ever flown on a jet plain at an altitude of 25,000 feet or more and looked at the horizon CAREFULLY for 30 seconds or more, you can actually SEE the curvature of the Earth because of your elevation.

It is curved, 4-Dimensional.
The result of a curved space time is gravity, and you can see its effects on light:
https://secure.wikimedia.org/wikipedia/e…

And there aren't absolute directions in our universum, to get an absolute direction for inside of our universe you have to be outside, inside you only can say "up" or "down" relative to your viewpoint.

You can "see" it. Take a picture of the stars in area where then Sun will cross. Then once the Sun does cross that area note their apparent movement caused by the curvature of spacetime induced by the Sun. These effects are too small to be perceived by the human eye and perceiving a continuum with time as dimension is physically impossible.

Take a baseball and toss it in the air (slowly to avoid air friction). Observe its trajectory. That trajectory is determined by the curvature of spacetime. Take two objects that are different weights and drop them...they fall at the same rate minus air friction...this is the curvature of spacetime.

Direction ie coordinate systems are arbitrary...you can pick whatever you want. In General Relativity and physics in general (excluding some special parts) we can pick what ever coordinate system we like, but we they are chosen carefully to take advantage of symmetries of the problem which can make life a lot easier. So you are free to choose up or down in any direction. Still works out to be the same result.