Why you perceive time the way you do is easy enough. At any "point" in time your brain (or any physical system for that matter) is influenced by the points before it. Play around with cellular automata and it kind of gives you a sense of how time can be viewed as a dimension similar to space.
>Are the laws of logic always true in every possible universe? Could there exist a universe where p|^p is not always true? One where the ratio of a circle's circumference and diameter is not equal to pi? I guess these things would be impossible to imagine, but is logic just a description of reality, or is reality an implementation of logical axioms?
The laws of logic are true in all possible universes (according to logic.) Can you imagine a universe where 1+1=3? Where someone has one object, and puts it next to another object and suddenly he has three objects? It just makes no sense. The "laws" of logic are not laws in the sense that things like physical laws are laws.