If all clocks slow down, then physical time, which is defined by clocks, slows down. Experimental verifications include the fact that muons reach the surface of the Earth before decaying, and the flying of atomic clocks in aircraft. Time dilation implies that time travel into the future is possible by going fast. Therefore a 10 year round trip at this speed, by Earth clocks, would last only 5 years of astronaut's time. The astronauts would therefore take 5 years to travel 10 years intothe Earth's future.
Relativity of simultaneity is another consequence of the constancy of the speed of light.
Events which are simultaneous for one observer, but seperated in space, are not simultaneous for another observer. The conclusion of time dilation and the relativity of place and of simultaneity is that one person's space is another's time, and vice versa. Hence time and space mix. They are therefore not fundamentlaly different. It is the observer independent reality of special relativity.