Yes, the speed of light can be exceeded but only in nature. As far as we currently know it will never be possible for beings to create anything that moves faster than the speed of light.
For time travel there are scientists theorising that travel into the future is possible but even these few folk regard travelling into the past as more than difficult.
Of course a relatively prosaic method of travelling into the future would be to get your body frozen with the appropriate frozen fluids and before doing so leave instructions for either the specific time or circumstances of your thawing out, i.e. when a cure has been found for cancer. There are stories of folk who were terminally ill who have done this but as yet there is no news of anyone having been revived.