Unit Auxiliary Transformer Protection.

Yes, of course a breaker is possible. But I think you mean an auxiliary transfo which is connected direct through the fuses to the output of a big generator. If you work out the fault level at this point (generator + feedback from Grid side) and get a cost for a breaker which can break that fault, to compare with the aux. transfo cost, you will find why fuses are used! Also, fuses will limit the peak current and probably open in less than half a cycle - limiting current squared x time to be born by transfo and its connections. A breaker will take several cycles, plus relay detection time.

about what percentage is kept for unit auxiliary transformer rating from that of generator rating?

Auxiliary loads are about 1% - 2% of unit rating.

The rating of the auxiliary transfo may depend more on the peak current during motor starting (voltage requirements for motor start) than on the running loads.

By keeping the peak current down, sequencing some of the motor loads can give a beneficial reduction in cost and space requirements of aux transfo.