How is this power rating calculation from the battery's internal resistance carried out exactly?
My guess is that it is based on the maximum power transfer theorem, hence the maximum power you can deliver to a load depends on the internal resistance of the battery.
How does the above calculated output power relate to the heat generation rate (W) of the battery that is also calculated from the internal resistance?
If the above guess is correct, then the power delivered is the same as the power dissipated in the battery itself.
And how does this theoretical output power (typically) relate to the actual battery output power available to the user in practice?
At maximum power transfer, the output voltage of the battery cell would be half of the no-load voltage. In addition, the efficiency would be 50% and hence a lot of the energy is lost in internal dissipation. For a practical case, the allowable voltage drop and criteria for energy efficiency would limit the power delivery. I have no industry experience on battery systems, but to increase the energy efficiency to above 80% or 90%, the power must be decreased less than 64% or 36% of the stated maximum output power value (again using the same theorem). However, the internal resistance will vary with several operating parameters, so my numbers are for an ideal case.