Ok I actually design/build/model transformers, they aren't 50/60 Hz transformers and aren't using sinusoidal power sources, but doesn't matter. A transformer is a transformer.
You gave me the following:
1) 50KVA rating
2) 0.8 PF (which I assume is at rated DC load otherwise it is completely arbitrary)
3) You gave me 10KW load
If you ask me to design/build this transformer I would need a lot more information. For instance I don't know what the transformers efficiency is so I don't know what the unloaded PF would be (estimate).
The inductance of the transformer won't change as a function of load ( more or less, small percentage), it's effective losses which are essentially in parallel with the load will change, principally because of heat and or perhaps some harmonics showing up in the current wave form.
As to running an inductive load, that's easy because it is just reflected back to the primary and is in parallel with the primary inductance. If that load is a motor then of course depending on the torque the motor is under, the PF reflected to the primary will change. A stalled motor represents large reluctance, small resistance, spun up then the equation is opposite.
So since you haven't really given me enough information. on your application, I am unable to specify the parameters..
FYI, manufactures of 50/60Hz transformers are really bad at specing a transformer. design in Engineering terms.
Sorry can't help.