It was an editing mistake by Shonen Jump. He was supposed to say "You are the product of a human and ---" both times, obviously.

I can believe Ichigo never went on to ask his dad all the deep backstory of his powers or whatever. Ichigo never seemed terribly interested in the nuts and bolts of all the wacky shit going on in his life and "my dad had similar abilities" seems like enough for him. He even says, when Isshin shows up during the huge Deicide battle, that he has nothing to ask his father. Isshin has basically estranged himself from his family with both the death of their mother and with his big secret. I can see why he never bothered elaborating - it would be a conversation that had to start with "So, about why everything I ever told you about myself is a lie and how I could have done a lot of good if I had come clean sooner".

I don't give a shit about Karin, Tatsuki etc since none of the foreshadowing about the bit players getting relevant combat abilities has ever meant anything and that is all he does with them besides Tatsuki's dyke crush on Orihime. Hell, even the major bit players like Chad and Ishida only get the ability to get the hell beat out of them by 2nd-tier villains and cry about Ichigo saving everything.