If the light beam contained within it enough energy that the beam itself exerted a powerful gravitational field, yes. However, getting yourself out of that gravitational field would be very, very, difficult,unless the light's dispersal would do it for you, in which case you just annihilated a planet-sized mass or larger to make your journey. Still, you wouldn't be dilated within the field relative to anything else not in the field, so...

A beam of light which was concentrated enough to cause this much twisting would be so intense that it would vaporize the spaceship instantly--and probably put a big hole in the planet, too.It would be much safer and more effective to put that energy into an accelerating rocket, which would also dilate time for people aboard. It wouldn't help you go backward in time, though, which would be the most interesting thing.

Great questions! If you're interested in Physics, take as much Math as you can. There are a lot of people (with web sites, of course) who claim to have "discovered" radical new Physics. The best way to find out if they're right or wrong is to solve the equations yourself--or at least to know enough to find out which side of a debate has the stronger foundation, with fewer assumptions. Maybe you'll be the one to find a hole in "established" Physics!

If a spacecraft were to have a sphere of light orbiting around it -- it would already be in its own space-time, such closed light-paths usually form around black holes. In general, though, the microscopic interaction of light and gravitation is not understood in any way other than the semi-classical limit (i.e. There is not a tested theory of quantum gravity-- indeed there seem to be very big problems in making any test of such a theory). However, as in all science, this can and probably will change with time.

One nifty thing about this generation is that it is possible for anyone owning a computer can simulate special relativity events. It is relatively easy to simulate special relativity -- for example what you'd see driving down a street at 0.85c ... One way to get an intuition is to build the Lorentz transforms and then model events with a much lower speed of light -- and observe the issues of time and space dilation first hand.