Em relação às questões 1 e 3: John viu (pela janela) os dois homens prestes a tomar os remédios. Ele assumiu que Sherlock iria engolir a pílula, então ele decidiu atirar.
Sobre a questão 2: Não sabemos, mas se Sherlock estava certo em sua dedução, havia apenas uma pílula venenosa. De wiki da Baker Street :
Summing up his observations, Sherlock ventures that the "game", as the cabbie calls it, is about his children. The cabbie confirms he has been estranged from his children for three years and has been told that he is dying. He adds that the inheritance he will leave for them is only meagre, And in that moment, focusing on his children and his mortality, the cabbie looks to the pill bottle on his left. Sherlock deduces that is where death is.