My very vague understanding is that nothing would keep the particles of the spacecraft together and they would fly off in random directions at lightspeed. Everything inside the area would be instantly annihilated in a flash of either elementary particles, or pure energy if the particles themselves are ripped apart.
No. The fact that it would take infinite energy to get an object with mass to c is a common explanation for why it is i possible to go faster because its relatively easy to explain and understand. At this point you already don't have to bother looking any deeper in the realm of acceleration and relativity.My understanding has always been that the problems lay in getting to c and in changing the velocity of an object that is currently at c.
But the whole problem does go much deeper. Within the current understanding of space time, speeds greater than c make no sense. c is not randomly 300,000 m/s, but is 100%.
Saying that something is traveling at 110% of c is like saying a box is 110% full. A 1000 ccm container can not contain 1100 ccm of stuff.
Another thing: It is not just the photon that travels at c, but also the electromagnetic force and gravity, and I also assume the strong force. If atoms would travel faster than c, they would move faster than the forces that bind them together. They would no longer be able to interact with each other. Atoms can't stick to other atoms; protons, neutrons, and electrons that make up atoms can't stick together, and the quarks inside protons and neutrons can't stick together. Anything faster than c could only exis as individual elemental particles at the most.