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In other words does it make sense to say that we live or exist in dimension x? Or do dimensions not apply to reality the universe its self?

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No, it does not make sense (we do not live in a dimension, but we live in a space spanned by x amount of directions). But your second question does not depend on your first question, so you should not write "Or". –  Chris Gerig Jan 21 '13 at 4:48
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In science fiction it's not uncommon to see phrases like "travel into the fourth dimension" as if the "fourth dimension" was something you could leave our universe and travel into. However this is not what the word dimension means in physics. The dimension of a spacetime is simply the number of co-ordinates needed to locate a point within it. For example to locate a point in our spacetime you just give its position and time $(t, x, y, z)$ so our spacetime is four dimensional (three space dimensions and one time).

So it doesn't make any sense to say we live in dimension x, but it does make sense to say we live in a 4 dimensional spacetime.

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well, if string theory becomes the theory of everything, as it promises, we are living in at least ten dimensions, the every day four and the atleast six curled up ones. –  anna v Jan 21 '13 at 8:10
    
There are those of us who (with absolutely no reliable evidence :-) suspect that the dimensionality of spacetime is an emergent property anyway. –  John Rennie Jan 21 '13 at 8:20
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