the further away from a strong gravitational force the slower time flows but it does continue to flow this was proven by placing one atomic clock 12 feet above another and after one year there was a measurable difference in the time so you can slow time but not stop it in space
Yes, but time flies. ;-)
Define "space" ?
Why would you need one?
I believe the question was hypothetical. I doubt very much that this man will ever actually need to use a watch in space.