Matrix "Multiplexing" with electromagnets, interesting behaviour
Of course, permanent magnets are attracted to the iron with no current flowing. Iron is ferromagnetic. 

If you don't have a more-or-less closed magnetic circuit, a lot of the field lines will go through the air and, if the cores (nails, in your case) are close then there will some effect on the nearby core when your coil is energized. 

You should have diodes across the coils (in parallel), reverse biased, of course, to prevent the (high voltage) turn-off spike from possibly killing the series diodes.