Can a fuel injector cause an engine to seize

From your description the damage is already done. What happened is that a faulty injector was dumping a lot of fuel into the cylinder. This fuel took up all of the space in the combustion chamber and when the engine rotated over the piston hit that fuel. Because the fuel does not compress the force bent the piston rod instead. This puts the piston in the wrong position and damages the cylinder. The misfire in cylinder five is related as the highly pressurized fuel that bent the rod very likely broke the head gasket between the cylinders as well.

The hard part would be to determine why the injector failed. That could be an electrical issue or a mechanical failure in the injector.

It would depend a lot on how it failed. Pulling the injectors to do a bench flow test might work but you could not be sure that removing them does not change the failure to a working unit. I doubt the freeze frame data that goes with the misfires would show anything but it might. You would need to look at the data and see if it shows the fuel trim trying to lean out that side of the engine in response to the over fueling issue.
Beyond that I do not know of a way to tell without tearing the engine down to actually look at the damage.
I would have an attorney look at that warranty as well. You might have a legal option that is not obvious.