space travel time dimensions?

Is it true that if we could travel the speed of light and went on a voyage in space that took a couple of weeks when we arrived back on earth years would have passed?
but would we not survive high acceleration if there was some inertia canceller in the spaceship?

Yep. Spot on.

Sort of, but you have one small detail wrong. You can't travel at the speed of light. But if you traveled at _almost_ the speed of light, then time would "dilate" just as you've described.

There's an equation that describes just how much time will dilate; it depends on exactly how fast you're going. If you want to stretch 2 weeks into 10 years, you have to go (if my calculation is correct) 99.9993% of the speed of light.

If you were to travel at exactly the speed of light, the same equation says that time in the outside world would stretch to infinity. That's one reason you're not allowed to do it. :-)

Yes it is true. There is a little problem, though. If you traveled on a ship that could provide a constant internal acceleration of 1g (like here on earth), it would take years to reach anything close to the speed of light. The instantaneous acceleration used in typical examples of relativity would not work for space travelers because we do not survive high acceleration.

The question is redundant, nothing can travel at the speed of light.