Does Hamlet see Claudius as a fatherly figure and is this one reason that he delays killing him until after his mother passes?

No, Hamlet definitely does not see Claudius as a father figure, and he doesn't mean to delay his revenge for so long.  Although Gertrude wants Hamlet to think of Claudius as a father, he does not.  When Hamlet kills Polonius behind the arras -- thinking and hoping it was actually Claudius -- Gertrude says that it was a rash and terrible act.  Hamlet replies, "Almost as bad, good mother, / As kill a king and marry with his brother" (3.4.29-30).  Such a line helps to show both how much he blames her for marrying his uncle as well as his suspicion of her and Claudius in the murder of his father.  He shows her two pictures, one of her dead husband and one of her new husband, and he contrasts them, calling one a god and the other a monster, respectively.  Hamlet makes her see that Claudius is nothing compared to Old King Hamlet, and she cries. 

Hamlet actually had the chance to kill Claudius in the scene prior when the king was alone and praying, but he decided against it.  Hamlet says, "Now might I do it pat. Now he is a-praying. / And now I’ll do ’t. And so he goes to heaven. / And so am I revenged" (3.3.74-76).  In other words, Hamlet almost kills him then, even drawing his sword, until he realizes that if he kills Claudius now, he would go right to heaven because he is praying.  Claudius didn't give Macbeth's father the chance to cleanse his soul before he died, and now he's trapped in Purgatory. Hamlet thus decides not to kill him now because it would not be true revenge: being sent to heaven is not payment enough for what Claudius did. 

He doesn't delay killing Claudius because he loves him; he delays killing Claudius because he first wants to make sure that Claudius is, in fact, guilty of his father's murder, and then because it isn't the right time.