No, this won't work. Light can certainly be used to send information through space, with one demonstration being NASA's laser-based communication system. The operating principle is essentially the same as using radio waves, but the shorter wavelengths (and corresponding higher frequency) in the light beam means greater data transfer rates. However, even a laser does not, and cannot, travel into the past or into the future.

Light can be used to gain information on the past state of an object (e.g., star or perhaps particles as in the question), because the light reflected from or emitted by the object takes some finite time to travel from the object to the receiver. If the object is very distant, then this is sometimes referred to as "looking billions of years into the past" because the light has taken billions of years to reach Earth and thus we are seeing the star as it appeared billions of years ago rather than how it appears now. BUT, the current state of the star is NOT represented by what we see; the light giving the information on the star right now is being emitted right now, and will travel for billions of years before reaching Earth.

There is one sense in which we can "move" through time, which is by looking at a range of objects, some very distant in space from Earth and others nearer. All will appear as they did at some point in the past, but as distance to an object increases so does the time between when the light was emitted and our "current" time, and thus the farther into the past we are looking. In the short distance limit, an object on the receiver can be viewed essentially in our present because light coming from it takes essentially no time to reach the viewer. The other limit, as already given above, is of an object so far away that it is seen now as it appeared billions of years ago. However, because even light takes time to travel through space, a laser directed at something now will not reach the target until some later time (i.e., not as it is now, when the laser is fired) and will return with information on the state of the object at "whatever time the laser arrives", not with information on the state of the object when the laser is fired or the state of the object at the instance when the light reaches the receiver (or, for that matter, on the state at some time in the future).

I'm also not sure what is meant by the laser "picking up information" on how far it has traveled or the surroundings. The distance traveled ("how far it's been") could easily be calculated since both the rate (constant at the speed of light) and the time since the light was emitted are known (and distance = rate*time), but any information regarding particles or anything else one might imagine would change the light would have to be transmitted to a receiver somewhere. Both of these steps, the light traveling to the particles and then traveling from the particles to the receiver, will take a finite amount of time; the person sending the laser beam will not instantaneously know that the light has changed somewhere far away.

One sort of time travel into the future which does occur is related to time dilation. For someone/some thing moving at very high speeds or in a region of very high gravity, time appears to advance more slowly than for someone outside. A practical application of this is in GPS satellites. These orbit ~20,000 km above the Earth and therefore experience slightly lower gravity than the surface. As a result, their clocks appear to run slightly faster than those near Earth's surface. This must be corrected or else accurately triangulating positions on the surface would be impossible.

We already use light to get information about the universe: starlight! Other than the sun, the closest stars to the earth are in the Alpha Centauri system, 4 light years away. So, the light from those stars gives us information about the star 4 years ago. In that way, it's like looking into the past.

All light that reaches our eyes gives us information about the past. Imagine you're looking at a tree that is 10 feet away from you. For you to see the tree, light had to hit the tree, reflect, and then hit your eye. This means that each photon of light from the tree that reaches your eye had to travel the distance between you and the tree. Since you are 10 feet away, each photon takes about 10 nanoseconds to reach you. So, when you see the tree, at each moment you are looking 10 nanoseconds into the past. However, at this point it's still impossible to look into the future :)

Your introduction includes a number of misconceptions. Among these are:
1. Lasers do spread out as they travel (although slowly), so yes, they lose energy with distance, and eventually become undetectable;
2. Light (including lasers) takes time to get somewhere, and then takes more time to get back. You cannot shine a laser into the past.

No, lasers as we can create them cannot be used for time travel. For time travel, you would need to go faster than light, and to our knowledge, this is impossible.