Info from the dude who have seen the datamine text dump
The 2nd one is most likely skills like Dance or Sing because it'd be dumb if it's inheritable. Pray that Desperation is not unique because only Shanna has it atm.I actually have a few ideas from the text dump.
Firstly, there will be limits to inheritance. Some skills can't be inherited due to weapon restrictions or movement type restrictions. Can't think of any examples though.
Another is that some skills can't be inherited since they're personal/unique skills.