Let me answer your second question first. In a steam power plant, you have a pump, turbine, boiler and condenser. The pump consumes power while the turbine generates power. Now it doesn't make sense to have a separate power source for the compressor when you have a power-producing turbine a few metres away from it. Hence, the part of the power produced by the turbine is used to run the pump. Hence the net power generated by the turbine is equal to the gross power output ($W_{out}$) minus the pump work input.
Next, to calculate gross turbine power output, you have to use the principle of conservation of energy. You are correct in that regard.
What you have calculated in the above equation is the turbine output per unit mass flow rate. Hence, you need not be bothered about the mass anywhere here. In fact, the units used by you are wrong. They should be kJ/kg. 568
Multiplying this by the mass flow rate of steam gives us the power output in terms of kW.
Next, what is enthalpy? It is the heat content of the system. How is the enthalpy increased? It is done by adding heat to the system. Hence, your change in enthalpy is taken care off in the heat additions as given.
Then, efficiency is defined as the ratio of the desired output to the given input. Hence, for the power-plant, this efficiency is given by the ratio of the net turbine work output to the heat added. Net work output, as stated already, is given by the gross turbine output minus the pump work.
Finally, the Carnot's Theorem states that 'll heat engines between two heat reservoirs are less efficient than a Carnot heat engine operating between the same reservoirs.'. Hence, to determine the maximum efficiency of the power plant, you have to replace your entire Rankine cycle set-up with a Carnot cycle working between the same two temperature limits. What does the term temperature limits refer to? The maximum and minimum temperatures attained by the working fluid during the cycle. Common sense tells us that the maximum temperature of the steam is right after it leaves the boiler. In this case, this temperature is $350^0$ C. Similarly, the least temperature is observed right after the water leaves the condenser. Now using these two temperature values, you can determine the maximum efficiency of the power plant using the formula for Carnot efficiency with $T_1$ = $350^0$ C and $T_2$ = $20^0$ C.
(Just do not forget to convert the temperatures to the Kelvin Scale !!!) 842