Schwarzschild Radius of a Galaxy If an ultra compact/dense Galaxy has a Schwarzschild radius same as it is own radius, how can it be observed from the outside of the Galaxy?
 A: If an ultra compact/dense Galaxy has a Schwarzschild radius same as it is own radius, it will have formed an event horizon around the galaxy. So, not only will the galaxy be unobservable for the rest of the galaxy, the inhibitants of said galaxy will be on an unavoidable trajectory towards collapse to a final singularity.
A: Such Galaxy would probably look more like one single mass-body, no empty spaces left in between, would you still call it a galaxy? 
Gravitational effects as usual can be detected,so its presence would still be inferred indirectly. If you are speaking about detecting it through light, then light bending such as the lensing produced might provide you with indirect detection. 
A: 
If an ultra compact/dense Galaxy has a Schwarzschild radius same as it is own radius

This is not possible. The Schwarzschild radius of a galaxy with say 200.000 solar masses is 590 km. Disregarding the fact that all stars would reach the singularity in very short time (for comparison 13 hours in case of 3 billion solar masses) the theoretical matter density inside the black hole would be much much higher than in case these stars are packed next to each other.       
