CSflim

Well, I wouldn't go so far as to say that time and space are an illusion, but the truth about them is certainly quite counter-intuitive.

Time does not "flow" unstoppable, like a river. There is no absolute time. We cannot say that two spatially separated events A and B happen at "the same time", as such a thing doesn't exist.

The classic example of this is the Twin Paradox, which is not really a paradox, unless you believe that there exists a "universal time", which is the same for everybody.
(The twin paradox: Two identical twins. One goes onto a space ship, and blasts off at near light speed around the galaxy. He returns some time later. As far as he is concerned, he has been away from earth for a year. His body has aged a year, and all of the clocks onboard, confirm this fact. However, at home his twin has aged by fifty years, and all of earth's clocks confirm that fifty years have passed. A paradox? Two clocks correctly given different times? No, not unless you believe in "universal time")

Further more, time doesn't extend backwards to "minus infinity". Time extends backwards, only as far as t=0. Before this time, there was no time.
Some people fail to see how you could have a moment in time, before which, there was not previous moment, but as an analogy, consider a journey to the north pole. When you finally get to the north pole, can you keep going north?

As for whether time is infinite in the forward direction, we have yet to determine. It is possible that time is finite, and the universe will end in a "big crunch", but at the moment, it seems that the evidence points away from this possibility, and towards the opposite, a total heat death, where time never ends, but the universe just keeps getting bigger and bigger, and colder and colder, and less dense and less dense.

As to whether space is finite or infinite, you have to realise that you cannot separate the two. Speaking of time independent of space, or of space independent of time, is precisely meaningless. Space and time are just manifestations of a unified "space-time". As such, if time is finite, so is space, if time is infinite so is space.

Further more, the true nature of "space", may not be directly as we appear to intuitively grasp it (it the same way that time is also counter-intuitive). I'm sure that you have heard before that "space-time is curved". The only way to easily explain what that means, is to use the classic example of a curved earth's surface.
If you look at the ground, it appears flat to you. You conclude that the surface of the world is a flat two-dimensional plane. Seems to make sense!
Until you realise, that the earth is actually round, and that the two-dimensional surface, is actually curved around, and so the ends meet each other.

Similarly with space. We see space as being "obviously" three dimensional and "flat", but in reality, the "three-dimensional" space-time is also curved in a similar manner to the curved two dimensional plane of the earths surface.

The question is, is it "positive" curvature, or "negative" curvature. In other words, is it curved in on itself, to create a closed "sphere" of sorts, or is it curved away from itself, to create a "saddle" shape?
This question is actually equivalent to the question "is space infinite?", which is equivalent to the question "is time infinite?" (See what I mean about not being able to speak about one without including the other?)

If space-time is finite, then it must be closed, like a "sphere", but if space-time is infinite, then it is open, like a "saddle", (alternatively, it could be a very "flat" saddle, making it a flat plane, which is also infinite).

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