Answer:
Brief answer to the questions:
• Waverly doesn't like it when her mother fixed her hair as it is hurting her.
• Waverly's mother means that the best torture is not about physical pain, it about mental torture.
Please see explanation below for further elaboration.
I would say that Waverly doesn't like it when her mother fixed her hair. I can tell this by the way how it was being described. She said that each morning her mother would "twist and yank on my thick black hair until she had formed two tightly wound pigtails." The text shows how Waverly felt every time her mother fixed her hair. By describing how her mother fix her hair by twisting and yanking and form tightly wound pigtails, this goes to show that she was hurt by the way her hair is being fixed. Thus, I would say that she doesn't like it when her mother fixed her hair.
"We do torture. Best torture."
For me, the above line said by Waverly's mother is more of a lesson than the harsh meaning of it. As we go through reading the story Waverly used different tactics and techniques to defeat her opponent without realizing that it is the "best torture" that she is doing. The best torture as being the most effective torture method are not actually the ones that inflict the most pain, but those that inflict the most psychological pain in order to mentally break the person being tortured. A person who suffers from mental tortures will be easily defeated by opponents, which determines Waverly's victories in chess.
Thus, I would say that when her mother said "We do torture. Best torture" she doesn't intend to mean the physical pain of torture but the mental torture. For her the best torture is not by inflicting physical pain but by attacking the mental aspect of an individual as this give the best torture.