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In a voltage circuit, the voltage remains the same. Thus when we add or remove the lamp, the total voltage at X will still remain the same. As a result, Z will light with the same brightness
Nope. Assume each bulb has a resistance of 2 ohms, so before Y is removed, X and Y have a combined resistance of (1/2)+(1/2) = 1 ohm
while after Y is removed X would have a resistance of 2 ohms, and so a higher voltage. Consequently, the voltage across Z will decrease and it gets dimmer