Remember that Q_dot and Q_dot_out are the same concept.
Data:
V_dot_1 = 3.333 m^3/sec, notice the unit conversion
k = 1.4
P1 = 100 kPa
T1 = 288.15 K
T2 = 308.15 K
T_L = 283.15 K
T_H = 298.15 K
Results:
A: Q_dot = 80.97 kW
B: W_dot_in = 4.07 kW
COMMENT:
"Assuming the air in the heat exchanger acts as a heat sink having an average temperature of 25°C", is a very bad assumption. It can do no such thing. If the fluid in the heat pump did its condensing at a constant temperature of 25 C, the air on the other side wouldn't ever get hotter than 25C.
The deal is, that with the Carnot cycle, the "high temperature" refers to the HIGHEST temperature that the "working fluid" needs to be, in order for the cycle to accomplish the goal. In order for a working fluid to heat air to the temperature of 35C, that working fluid must be HOTTER THAN 35 C, somewhere in the cycle.
This means, the answer to part B, is really 6.57 kW, despite what the question said.