no time dont stay still. acording to the real Einstein the speed of light slows down time for example our high powered telescopes take photographs of other galexies and those photographs are really from more than billions of years old but it depends on how far away it is
Yes, if you were traveling at the speed of light, you would experience zero time flow. If you could be turned into pure energy, and beamed across the galaxy at the speed of light, it would take almost 100,000 years earth time to send you across, but once you were reconstituted back into matter, you would not have noticed the change in time. To you it would have seemed instantaneous.