Speaking from a standpoint of relativity:
A) Give a definition of "Time."
Time is another dimension, somewhat different from the spacial dimensions. To better understand time, we must first define the "light-cone." The light-cone is the locus of all points in space time relative to a given base point that have the following properties:
1) The point is at relative rest to the base point.
2) The point could be reached from the base point by traveling at a speed less than the speed of light (for the future light-cone), or the base point could be reached from the point by traveling at a speed less than the speed of light. In other words, |Δd/Δt|<c.
Thus, the future light-cone is the locus of all points in space-time that are definitely in the future of the base point. The past light-cone is the locus of all points that are definitely in the past of the base point. Points on the edge of the future light-cone are either in the present or future of the base point. Points on the edge of the past light-cone are either in the present or past of the base point. Points outside the light-cone may be in the past, present or future of the base point. The last three possibilities depend of the relative speed to determine where they line up.
The purpose of the light-cone is to provide a definite order to events in time. What it doesn't do, however, is explain in which order events occur (past to future, or future to past). To give order to time, we must use three "arrows of time":
1) The Thermodynamical Arrow of Time - Entropy increases as time progresses.
2) The Psychological Arrow of Time - We remember the past, but not the present. Note that this arrow can be shown to actually be a direct result of the first arrow.
3) The Cosmological Arrow of Time - The universe is expanding.
These arrows need not point in the same direction, but, through a proof that I will omit (if you really want it, I'll give it), these arrows must point in the same direction if intelligent life is to form.
Explanation of Explanation: The lightcone portion is to define how time orders (sometimes) events into a past, present, and future. The arrows portion defines the difference between past and future.
B) Where did time originate?
Time is an intrinsic property of our universe, and was most likely created along with it. It's important to analyze the space-time curvature of the universe in order to show how it might look from outside our perspective of time. There are three possible curvatures:
1) Positive - The universe expands at first, then contracts in a Big Crunch. From outside, it may look like a hypersphere (a multidimensional version of a sphere).
2) Negative - The universe expands, and keeps expanding at a more and more rapid pace. It would "end" by becoming progressively thin and fading away, with a few black holes remaining as collections of matter.
3) Flat - The universe expands forever, but the rate of expansion keeps decreasing, so it approaches a final volume. Eventually, entropy and black holes would take over, causing a "heat death."
It's important to note that in the latter two cases, all that will remain will be black holes. Since black holes are most likely singularities, they have the possibility to sprout into new universes--maybe.
I'll leave part C to someone else.
Just a warning about copyright infringement: material placed in the public domain (such as this post) is automatically copyrighted, so you can't use what's been said here without citing it, unless it's common knowledge. I could, in theory, go without citing this as I'm not claiming it to be my own work, but since you may want to use it, I'll tell you that pretty much everything here is from Stephen Hawking's A Brief History of Time. The part that isn't is my analysis of the shape of the universe. This part is mostly my own (stemming from what's "common knowledge" in the theoretical physics community), and I can get into a lot more detail of my theories if you wish, but they don't pertain directly to time. Most of what is said here could be considered common knowledge, but be careful.
