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short answer:
senario 1: not throw because you are trying to win

senario 2: game throw. There is a difference between might and must. Unless the vigi is trying to prove his role, in that case the vigi should explain the reasons for shooting the seemed-to-be invest not only after being reported, but also in the game so as to let town know that you are helping.
If you are a confirmed vigi then you should do this even less. Unless town is on the verge of being overpowered and gambling is your best choice.

senario 2.5: if the lynched evil is being suspected anyways, then it's not gamethrow. It's just usually people don't plan that tactic more than 1 in-game-day ahead of time.

senario 3: i would not call it gamethrow, the reason is: vigi shooting a town who is gonna be lynched by town the next day effectively eliminates a night which evils can attack, which in your case ends up saving 1 life.

senario 4: i don't think so, because in that case amne converting into jester is gamethrow? it only says your role's win condition, didn't say about sticking to your original role. PLUS at the end of game usually everyone (alive) can be converted to cult, you just have to lynch cult during day to get more space.

short answer:
senario 1: not throw because you are trying to win

senario 2: game throw. There is a difference between might and must. Unless the vigi is trying to prove his role, in that case the vigi should explain the reasons for shooting the seemed-to-be invest not only after being reported, but also in the game so as to let town know that you are helping.
If you are a confirmed vigi then you should do this even less. Unless town is on the verge of being overpowered and gambling is your best choice.

senario 2.5: if the lynched evil is being suspected anyways, then it's not gamethrow. It's just usually people don't plan that tactic more than 1 in-game-day ahead of time.

senario 3: i would not call it gamethrow, the reason is: vigi shooting a town who is gonna be lynched by town the next day effectively eliminates a night which evils can attack, which in your case ends up saving 1 life.

senario 4: i don't think so, because in that case amne converting into jester is gamethrow? it only says your role's win condition, didn't say about sticking to your original role. PLUS at the end of game usually everyone (alive) can be converted to cult, you just have to lynch cult during day to get more space.