what human feelings do androids possess and lack?

Yes, the main thing is empathy test or Voight-Kampff Empathy Test was used to determine if a person was indeed an android. The manufactured people were identical to naturally born people except for a few very important things. Because they had no memories or vague implants their emotions were unstable. They had all the feelings that naturally born people had, they lacked the ability to handle the intense ones. This is partly why they had the four year life span; they tended to go insane after that point.