I suspect my view is similar to your own: with these sorts of behaviours still going on at 7 years old, it could be evidence that your DD has ongoing special needs and therefore may always be difficult to parent. On the otherhand, she could be late maturing.
One of my DDs was very challenging to parent at home (in different ways from yours). This raised similar questions in my mind to the questions you have. There had been some trauma in her life, which in our case was a possible explanation for her difficult behaviour. I organised a series of sessions with a child psychologist when she was 7 to get a professional view. The psychologist's view was that she was late maturing (several possible explanations) and hypervigilant (response to the trauma).
My DD is a bit older now; still challenging to parent at home (terrifically well behaved during class; not easy at after-school club) but her temper outbursts are getting less dramatic and more infrequent. The stressors in her life have been much less now for approximately a year, and she is older, so I plan to insist on better behaviour this school year. Up until recently I felt that I had to re-build her shattered self-esteem, which made parenting her temper tantrums really tricky. Fortunately her self-esteem is much healthier now, so I think I will be able to be stricter and call her out when she is behaving like a much younger child.
I think time will tell with your DD, but you might like to get a child psychologist's view in the meantime. Try to find a good clinic. Unless you're prepared to wait a very long time for the NHS waiting list (and convince your GP that her behaviour is very concerning), then you'll need to pay privately.
In the meantime -- the psychologists and therapists I've spoken to formally and informally confirmed that it is very important for the child's future life (adulthood) that their parent/s act in a mature way - modelling appropriate behaviour and communication during highly emotional situations. It is also important to the child's development that the parent stays in charge.
Proportionate rewards, consequences, lots of hugs (even in the middle of a stand off - to see if you can get past her barriers) and tonnes of patience are crucial. Hindsight humour is also helpful! Some of the tantrums and things she says are in hindsight pretty funny.
Try and figure out some of her 'triggers'.
It's exhausting, isnt it?! True parenting!