Answer
(a) Bulb A is the brightest while bulb B and bulb C are equally bright with each other. That is: $~~A \gt B = C$
(b) Bulb A gets brighter. Bulb B and bulb C will both go out.
Work Step by Step
(a) The power dissipated by a bulb is $P = I^2~R$
A bulb's brightness depends on the power that is dissipated.
All the current passes through bulb A, but only half the total current passes through each of bulb B and bulb C. Therefore, bulb A is the brightest while bulb B and bulb C are equally bright with each other.
(b) Since the resistance of the new wire is essentially zero, all the current will flow through the wire. Since no current flows through bulb B and bulb C, they will both go out.
Since the resistance of the circuit decreases while the voltage remains the same, the current must increase. Then the power dissipated by bulb A increases, so bulb A gets brighter.
