Lights are something I understand. They're connected with the train network so that the train, traffic, and pedestrian flows can very relatively balanced. Its called a partial priority signaling system, because trains are given a higher level of priority compared to other traffic, but their presence doesn't imediately trigger their right of way like on the other lines. I don't know why the east/west section is blocked off, but I bet they can't activate the lights until they're tested and certified to work properly within the broader signal network.
As for why lights were added going both directions, here's my guess: North/south so that pedestrians can cross without worrying about traffic and trains, and east/west so that idiots don't drive into the trains while trying to turn onto, or cross 83rd.