The copper loss (1%) is proportional to the square of the load factor, what do you mean by that?

Copper losses have a dependency on the load of the transformer. The dependency is quadratic depending on the load factor. Example: 

If the load of the transformer is 90% (load factor = 0.9) of its nominal load (Snom), the copper loss of 1% (x) will be: x*Snom*0.9², so multiplied by 0.9². Therefore, the copper loss is only 1% if the transformer is running on 100% of its nominal load.