My oldest is 21, youngest is 8, all girls, BTDT. If they told me "no", they had to sit with their fingers on their lips in the "shhh" sign for as long as their age. No talking, no squirming, those would add minutes. "You don't tell your mama 'no'".
They also learned very early on that my "no" meant NO. In the Bible, Matthew 5:37, it says (and I love this!

), "Simply let your 'yes' be 'yes' and your 'no', 'no'" and that has been my rule. If I said no, even if it was on a tired, I don't really want to answer you, unreasonable mood, it was still no. I would not have allowed the book, even bought with her own money TODAY. It would have been something she could buy with her own money on the next trip. Cleaning a room at my house just goes with the privilege of living there, it does NOT earn you anything, but a clean room and a happy mom.
As far as room cleaning goes, I think that's still a little young to do it alone. My 8yo still has moments where she just needs some guidance. Once mine were old enough, if they didn't do it, I did, but with a box or garbage bag. A time or two of that was enough.
Getting in the car? She's not too big to pick up. Mine had ONE chance to get in the car when told, then they were firmly picked up and placed in their seats. Whine, cry, moan, and groan all you like, but parking lots are dangerous places and you're going to OBEY the first time around when I tell you to get in the car.
She will outgrow it, but I can guarantee that the next stage is just around the corner and this one is just preparing you (and her) for the teenage years. The groundwork you lay now in your discipline will be what keeps you (and her, but she'll never admit it) sane in another 10 years or so.