Econ assignment question

[tabako]

A(y) B(t) C(h) w payoff (4,3,7)

This can't be an equilibrium because if A does strictly better if he goes x instead of y. I understand this might seem sort of counterintuitive because A can't know whether B will z or t because he is indifferent between the choices, but the equilibrium concept doesn't "care" about this. I don't know the best way to explain this, but I know its not an equilibrium solution.

Your other two paths are right.
I haven't seen the complete strategies notated as you presented them, but it makes enough sense.