Averaging 1 min kW values
Averaging (i.e. taking the mean of) a bunch of numbers do not change their units. Just like the average length of 60 sticks with a length in feet is some value in feet, the average of 60 values in kW is a value with units of kW.

So,


Yes, if you take the mean of the first 60 values (in kW), you will get the average power (in kW) during the first hour.
No, but: the energy is the mean power multiplied by time, and if your time is one hour, the number is the same but the units are different. 50 kW times 1 hour is 50 kWh.
No, as above, but also your unit is a bit confusing. See below.


Watts and kilowatts are a measure of power, which is energy divided by time.

Energy is therefore power multiplied by time, measured in kilowatt-hours (one kilowatt of power operating for one hour).

You talk about "kilowatts per half hour", which would be power divided by time, and represent something like the rate of change of power. I believe you meant an energy unit like "kilowatt-half-hours" (a kilowatt of power operating for half an hour).