Light speed... not really to much to say about that other then you are traveling at the speed of light. However, has it does relate to time travel I do know a this:
The farther away a person is to any given point the easier it is to time travel. In fact we are currently time traveling right now. Every step me take and every turn we move is a travel ( in a way ).
Its like this:
Lets say that if I was here on earth and you where on a planet 100 trillion light years away time travel for us would be has simple has you turning your body or walking forward. Now, to you and me it would not feel any different then any other time. However, if you where to travel back to earth after you move around a little bit you might find yourself in a whole ther earth.
Granted, this is all relevant if you have the ability to travel the seed of light.
When you look in a mirror you are not looking at the present you! You are looking at a past you. It takes time for your eyes to retain the mirror image. That is how close time travel really is to us already.
Has for speed of light ... don't really know, sorry!