Growing Out of Toddler Behavior...

Oooh yeah. Girls do all those things at that age. My oldest daughter is 6 and my youngest is 2 1/2. The youngest is much more fiery and temperamental (she's still the master of the quivering lip and silent cry face), but even the older one did all of this. Or rather "tried it". We clamped down immediately on bratty tones and actions just to prevent escalation. At almost three, yes it's developmentally normal, but also NOT AT ALL too early to discipline it and prevent lots of future drama. It's actually the CRUCIAL time to. Kids this age are brilliant and very fast to learn if you are CLEAR with them. My youngest had an extremely angry difficult personality ever since age 9 months (tantrums started a full year sooner than older two) and even she won't execute a full blown tantrum or mean angry action like hitting or throwing at a parent or fellow child because of (very) early discipline. I love the book Back to Basics Discipline by Janet Campbell Matson. All my kids snuffed those yucky aggressive phases really quickly with effective discipline which enabled us to keep things positive and happy most of the time and avoid terrible twos threes and beyond.

I think she's too old to still be flinging toys, unless she is developmentally delayed in some way, but it doesn't sound like she is.
Sounds like you need to establish some firm boundaries, and then ENFORCE them. For example, make it clear that throwing toys is NEVER ok, and if she does it, use whatever discipline works best for her. She sounds like a little drama queen (lol!) so I bet putting her in a time out and not looking at or speaking to her for three full minutes would be effective.
Does she go to daycare or preschool? How is she around other adults? If she listens and behaves well for other people but not at home then you know it's not "normal" behavior, she's doing it because she CAN.

We do not throw toys.
We do not hit .

You seem frustrated, would you like to sit here for a few minutes, or go to you room for a few minutes?

Very normal. Our daughter was also a very verbal child with a high comprehension. She knew the rules, so we would ask, what is the rule?

Or we would ask her to "use your words". Luckily at her daycare, they also used this same language.

It's normal behavior, she'll test boundaries. Perhaps the reason she'll tell you nothing is wrong when she's clearly upset is because she doesn't (yet) have the words to express how she's feeling. My daughter (almost 4) is also very verbal and would throw things and sometimes hit or try to hit when upset (still does on occassion). I've found that helping her identify her feelings and validating them can diffuse a lot of her emotional upheaval -- not always, but it's worth trying.
Reminding her of the rules is a good method, too, if you know she already understands the rules /expectations, since this is learned behavior and needs practice to master.
Giving choices with consequences can be effective, too -- 'would you like to sit here for a few minutes, or sit in your room for a few minutes?' -- giving her a sense of control, which can help restore some calmness.

Hope that's helpful, all the best to you!

She sounds pretty normal to me. I would suggest that she gets a consequence, such as a time out EVERY time she's aggressive. If you are inconsistent with consequences she will continue to test you.

Sounds developmentally appropriate to me.

One thing you can do is tell her about more appropriate ways to express her frustrations and anger.