Phantom power is a power source for high-end condensor mics that need extra voltage that a normal pre-amp doesn't provide. The condensor mics do not work on the moving coil principle that your SM57's use (acoustic energy pushes coil in to create corresponding current); rather they use fixed plate systems that conduct electricity on a suspended coil. Because such miniscule movements (one plate moves in relation to the other) as compared to the moving coil design, the resulting generated current is at a far lower level than what would come out of a SM57. So, phantom power is provided to boost this signal to line level that the recorder or signal device expects to see. (in short - use it for condensor mics if you've got 'em, dont if you dont).
As for playback levels, the accepted standard is 85 dB, which if you cant find your dB-ometer, is roughly equivalent to normal playback level on a home stereo. However, I suggest playback should be done at various degrees of loudness, as you can discover EQ deficiencies present at lower or higher volumes - check anything you mix down at varying levels. Cheers!