1. The building is
Battersea Power Station. In the movie it was converted as a government refuge to safeguard works of art from around the world due to widespread anarchy. The building is most famous for being featured on the cover for Pink Floyd's Animals album.
2. FISH was a countermeasure to the totalitarian government and their treatment towards immigrants in particular.
3. The FISH agents had to blow a hole in the wall to get inside the complex to intercept the baby going into the boat. That explosion was the X factor that caused the rest of the incarcerated immigrants to unite, I'm sure they were already ready and just waiting for an opportunity to break some skulls though.
4. The rest of the world has gone to shit because humanity has lost hope in the future(there was a propaganda tape while they were on the bus that showed major cities in complete chaos that ended with the slogan "Only Britain soldiers on"). Because the rest of the world has gone to shit, everybody wants in but Britain's afraid that the immigrants will bring the same chaos to them. The immigrants don't take kindly to being treated like shit so some of them fight back with terrorism which escalates the tension.
5. They wanted to take the baby to the ship so they could rendezvous with the Human Project, an institute independent from the (corrupt) government that's treated them like shit(the mother was an immigrant or immigrant descendant).