Gravity manipulation is already being done in huge numbers of ways so that one is easy. Spinning manned space stations, the "vomit comet". G-force manipulations for different purposes...All technically "gravity manipulation"
Time travel is also done already to an extremely small extent. The proof is in the fact that 3 atomic clocks were set to a specific and matching time. 1 was kept in London. 1 was kept in New York and the 3rd was on a plane travelling between the 2. It was noted that because of the speed of travel, when the plane landed, the two clocks on either side of the Atlantic were still identical but the one on the plane had changed by 3 millionths of a second. It was called the Hafele-Keating experiment and it was designed to prove some aspects of special relativity.
http://en.wikipedia.org/wiki/Hafele-Keating_experiment
A for a death star type weapon. Simply not enough resources on this planet to build one so it would take some of the other technology to do it. i.e planet terraforming and colonising of the solar system. (both of which i believe will be possible within 50 years)
Figuring out how the universe started has been done whether some people accept the big bang theory or not. The evidence for it is huge. Just because some people don't understand it or want to doesn't make it untrue.
Creating matter?
http://web.mit.edu/newsoffice/2005/matter.html
Faster than light for objects with mass I believe will always be impossible given that for an object to travel at the speed of light it would have infinite momentum. To achieve infinite momentum it would either need to have finite acceleration for an infinite period of time or infinite acceleration for a finite period of time. Neither of which is possible.
Particles with no mass, if I remember correctly, have already been made to go faster than light but only through medium which is not a vacuum and so doesn't condradict relativity.