Unless the shop misplaced it, it will come with a manual, some just a small piece of paper. But most manual provide unnecessary or unuseful info anyway. So no one use or keep the manual either.
Active circuit as the word means, it needs external power source to have an output. Some times 9V or 18V (1 or 2pcs 9V battery)
Active pickups so far most likely means EMG brand. Others are normal pickups with an outboard preamp circuit.
Active is good for strong signal and less degrade in quality over a longer cable length. The tone wise is not suitable for all type of genre of music.