Nodes vote with their hash-power on the branch of the chain which they consider to be truth.
Only correctly functioning nodes do that.
Evidence of byzantine failures is the existence of multiple branches; we call these orphans. Each branch presents a different version of truth to observers of the system.
Not really, those are just evidence of latency. If a majority of the CPU power is conspiring to attack the system and all non-cospirator blocks are orphaned then no one will mine outside the conspiracy and there will be no such orphans (there may still be forks within the conspiracy if they still have latency).
The system will have failed, but it will have failed
because it exceeded stated limits.