So Sheila IS Livi's biological mother?

yes. he just takes after his dad more than his mom

yes, he just calls her by her name and not mom for some reason.(〜￣△￣)〜

I feel like he calls her that to not associate her as his mother who had a child with the king. Everytime he would say mom (or any other variation) that would remind him that the king (the man he absolutely hates) is his father.

At least that's what I'm getting from this.

interesting point