How does a passive sonar (WWII) estimate the distance to target
 

Is it possible for a hydrophone operator (no active sonar) to judge the distance to a surface ship and if it is closing or going away?

I understand how he gets the bearing and the speed of the target but i'm not sure about the distance. How much detail can he get on a WWII U-boat.

If you can get bearing and a reliable speed, you can calculate range based on bearing rate. To get a reliable speed estimate you would have to know how many turns of the shaft per knot of speed for the contact.

As far as determining if a contact is opening or closing, that would be based off of noise of the contact. Quieter opening, louder closing.

All this only gives an estimation though and you would still need visual observations on the target to obtain a firing solution.