One issue is small particles in space (micrometeorites). While the space station may have managed to avoid catastrophic impacts over a decade, the probability of a major impact on a ship traveling for centuries at even a very small fraction of the speed of light hitting *something* in space becomes extremely high.
Citation needed. Outside of star systems I think the chances are more like fat and slim.
At those speeds, a golf ball size object
The chances of hitting a golf ball sized meteorite in the vast emptiness of interstellar space is infinitesimal. The point remains however. It just wouldn't be anything nearly that big. It would be a matter of deflecting tiny particles at around 0.1c. Not an easy task, but certainly doable. Perhaps whatever is used for radiation shielding (lead lined water tanks perhaps) would have enough mass to deflect such small particles. I believe that most of the particles would just be hydrogen atoms. There isn't a lot of matter out there.
You would need some sort of powered force field- a technology that does not exist and has no known theoretical basis for its existence.
That is ridiculous. You don't need imaginary tech. You just need some deflection mass. A large steel plate pushed in front of your ship would probably do the trick.
Another issue is food and biology. Previous attempts and creating a small closed ecosystem (biosphere) were miserable failures.
And of course any task for which there are failed attempts is impossible. We'll figure out the closed ecosystem thing. We'll have plenty of time to do so while we build our enormous spaceship filled with nuclear bombs at a lagrange point.
But even the generation ship must provide power for centuries.
I assume you are talking about maintaining electrcial power for hundreds of years. This is easily done with RTGs.
A final concern is one of need.
The need is the curiosity of any intelligent species. Our need to explore the universe. That is the only need required.