The math says that if you travel faster than light you travel into the past. However most physicists don't really believe in it; it's just fun to speculate about. There are frequently solutions in math that are not physical. For instance, there is a mathematical solution for spring motion that says as time goes on, a spring will oscillate with more and more amplitude (like a swing would just naturally swing higher and higher). However, we know that this isn't physical, and we pick the solution where the spring's amplitude decreases (much like if you were swinging high on the swing and it starts going lower and lower as you stop pushing) as the physical solution, even though the growing amplitude solution exists. It is just the time-reverse of the real physical solution (if you set time going backwards, you see that one solution just becomes the other). Likewise, there is a time-reverse solution for things that go faster than light that move in negative time, but as of right now no-one takes those seriously, just like no-one takes the exponentially growing solution seriously. the name for particles that have this property in quantum field theories are called "tachyons" and naturally move at infinite speed when they have no energy, and at the speed of light if they have infinite energy (sort of the reverse of us... if we have no energy, we move with no speed, and an infinite amount of energy will get us moving at light speed). And usually they're an indication of a bad theory.

Slowing down light does nothing for you. Just because you slow down the collective motion of photons doesn't mean you've changed the laws of the universe. The fact that light moves at the speed of light is caused by the universe, not the universe changes its laws according to how you change the group velocity of a bunch of photons. The speed of light is really a fundamental property of the universe, and light (as well as other mass less things) just happen to move at that speed in a vacuum. Its because of the universe that light travels at that speed, not the other way around. So no, slowing down light itself doesn't do anything for you, since it doesn't modify the property of the universe that there is a fundamental speed that all reference frames agree upon.