Yes, light exerts pressure on things, yes photons have momentum, yes solar sails should work in theory.
If you have light trapped in a bottle, and the bottle moves, then relativistic effects will mean that to the bottle, the light has a higher frequency on on end than on the other. Momentum for light is proportional to frequency, so this gives us our net force, but this net force is always in the direction opposing the motion of the bottle. Thus this idea could be used to decelerate spacecraft once they were more than halfway to their destination, but it couldn't be used to increase velocity, unless there's a clever frame of reference trick I'm not seeing, or microwaves are allowed to leak from one end and not the other (costing energy.) The deceleration usage still seems like a violation of conservation of energy hax, but at least it should only work at relativistic speeds or very high energy flux. OMFG I just got it, he must be using a refractive medium so that when light goes in one direction, it bends its path to turn around instead of being reflected. Actual momentum transfers only in the case of reflection, not refraction. In this case I must admit this is an uber physics hax. Except that wasn't described in the article, so maybe I should go patent it real quick.
http://83.219.63.174/Articles/295931/Microwave%20engine%20gets%20a%20boost.htm
Shawyer cautions that the calculations only work for static thrusts. ?You can?t beat the laws of physics. If it is used to accelerate, the Q value drops. It is best used to lift a body and oppose a force, for instance to counteract gravity. It cannot be used to accelerate further.?