I would think that she's not "manipulating" you as much as she knows when she says that you give her a big response.
She sounds like my daughter, a wonderful person, C. and usually good but sometimes naughty and will laugh if you punish her.
I have learned that laughing is my daughter's way of coping with being reprimanded. She's not really saying "haha, what you're doing is so funny" and she's not being manipulative, but rather she's choosing not to confront what she's done.
I have learned to let some things be taught to her by natural consequence. Lessons seem to be remembered much better that way. I have learned not to give her "lectures" but rather to ask her questions. "Was what you did a good idea? What happened as a result? How can you fix it?"
My daughter has been repeating phrases that cause reactions since she was a little girl. Any phrase that causes some kind of reaction she LOVES to use. Sounds like your daughter discovered that if she asks "do you hate me?" that you will give her a big reaction.
So next time she asks, don't give a big reaction. Instead, say "Do you know what 'hate' means?" Let her answer. She will probably say "It means you don't like someone" or something to that effect. Then you say "Do you think that I hate you?" Let her answer. You'll know by her answer if she's toying with you or if she seriously thinks that you do.
By taking the emotion out of it, you can find out why she is asking. She may have a definition of hate that makes her think that you do hate her.
I have learned to take the emotion out of my response to things that my daughter says. It keeps her from repeating them just to get some kind of reaction, but I can address her true feelings as well and help her to understand them.
My daughter was 8 and she got reprimanded and then went on about how she wanted to DIE. Instead of giving a big reaction, we explored her feeling and we discovered that she didn't really want to die ;) She never tried saying anything like that again, but I'm sure if I had reacted big, we would have gotten her to state she wanted to die every time she was reprimanded!
Good luck!