Darth Vader discovers that Luke is his son in episode 5 on the Cloud City of Bispin. Actually he probably already knew that but that is when he confronted Luke about it with he infamous "Luke, I am your father." Yes he does harbor paternal feelings very deep down inside him. This is evident when Luke is being tortured by Palpatine with force lightining in episode 6, Return of the Jedi. Vader picks Palpatine up and throws him into the core reactor of the Death Star. I don't think even Palpatine survived that.
Darth Vader also discovers he has a daugther in Episode 6. He senses it while he is trying to get Luke to fight him in order to help convert him to the Dark Side. Of course threatening to turn her to the dark side upsets Luke enough that he finally fights DV.
It should also be recognized (not 100% sure though) that DV never knew he had children. He was told that his child died with Padame.
btw, I'm not a hardcore Star Wars fan those questions were just easy

The hardcore fans are the ones camping out the movie a week in advance and read every single book the franchise has ever made. Those guys are the "hardcore" ones lol. I do love Star Wars though.