Yea I think it's a wee bit more than a theory... obviously when he goes into a black hole we can only speculate what that might be like, but in terms of the space-time relationship addressed in the movie e.g when they go to that tidal planet, and the guy left on the ship ages a lot more, that is proven theory now. That stuff is for real - if you travel near a very large mass then the time effect will be very different.
You can probably google this, but I'm sure some physicists actually recommended that Interstellar be shown in schools, because a lot of the physics in it is explained very well, and very accurately.
It sounds crazy but basically, physicists now believe that time travel into the future is definitely achievable. We just haven't reached the level of technology just yet i.e. interstellar space travel
That's not so much time travel as it is an illustration of how our everyday experience of time is flawed. Time does not exist independently of the observer, it is physically tied to the observer's frame of reference. Travel at near to the speed of light would create effects which are analogous to time travel into the future from the perspective of observers traveling more slowly but it's not time travel in the popularly understood sense of the phrase (transitioning from one point in history to another without experiencing or physically existing in the intervening period).
Re: real world applicability of those ideas, look no further than GPS. It literally would not work if relativity wasn't taken into account
http://physicscentral.com/explore/writers/will.cfm
People like Coldplay and voted for the Nazis. You can't trust people.