Question about relationship between time as discussed in Relativity in Physics, and time perception Its very relevant that the physicist you asked mentioned that no particle with mass can travel at the speed of light. You cannot discuss the possibility of traveling at the speed of light without it because they inextricably linked.
Speed is measured in relative terms to the observer you could travel near the speed of light relative to an object in space but relative to another object in space you could be still. Light however will travel at the same speed no matter the frame of reference. Only light or other massless particles can do this.
Since speed, relative to another object in space determines the time difference the two objects experience, and objects in space can be traveling at different speeds relative to one another. If you were to travel at the speed of light relative to the earth. You would experience the universe in a different sequence of events since time would pass differently at different point in the universe depending on their relative speeds and position in space to you.
As for if a spaceship could travel like light does in the same speed in in all frames of reference. Then we can only guess. Relative to an observer you would be not appear to change at all. In your own frame of reference the universe could blink out of existence is one possibilty but you would likely still age normally in your own frame of reference. But then in a light particles frame of reference the universe would have to also occur instantaneously. Its hard to say. There is likely a lot of physics we dont yet understand on this.