Backdooring his employer's code would be directly related to his work, and illegal actions on his own time would make him unemployable if caught and convicted, because he'd go to prison. False equivalances, all.
It depends entirely on his contract - I'd expect most CEOs to have a clause about their conduct causing harm to the organisation. Even if not, it's legal to convince someone to leave, which is what usually happens in public embarrassment cases.
No it's not. Indeed, you run a legal risk in NOT firing such a person given that keeping them around (especially in a senior position) creates a demonstrably hostile work environment.
