It is helpful to preheat crucibles to drive of any moisture that may have been pulled out of the atmosphere during manufacturing, storage, shipping, and cooling from the previous firing. And for high value fires (like refining), it is good insurance
Coating the inside of the crucible probably does not help. If you want to coat the inside of the crucible with borax, go ahead as it probably will not hurt anything. But, the borax is a low melting temperature component so the coating will not form much of a barrier after you start heating things up. And, it may "cost" you one of the fires.
Some people do some refining in assay crucibles. The fire clay used in assay crucibles is not rated for nearly as high of temperatures as graphite or silicon carbide, and this is not really recommended. But, if you have had success doing this, make sure and preheat the crucible before use (as mentioned above).
Preheating can be done by placing the crucible on top of the furnace, or on a hot plate, or by putting them in the furnace and raising the temperature slowly.