I'm not sue what you mean by "to a certain degree". The only way to curb these behaviors in healthy, intelligent, very spirited kids this age is with firm discipline to the degree it takes. Otherwise, you have to either suffer the behavior and become understandably worn down and enraged, or make a conscious choice to accept the behavior as normal and be patient about it until it is out-grown, while managing it with milder things like time outs that let you "do something" even if it's not stopping the behavior. Positive programs like Love and Logic work for some, but for a spirited child, you'll be able to tell if it's working or not once you use it for a while, and if it isn't, you need to ratchet things up, or accept things as they are.
Discipline saves my sanity, and I actually enjoy being with my 3 kids under five 24/7 while their dad always travels. I take them on every errand and I never get a break. I have a babysitter only once in a blue moon. Time outs weren't invented when I was little, and I haven't seen them be effective in people I know, so I cant' speak to sticking with something when it's not effective. 2 1/2 is very much old enough for self control and comprehension for these things, you are right, she knows what she's doing. Using ineffective discipline is almost worse than using none, because she's learning your "best effort" can easily be flouted, and she has nothing deterring her from continuing the behavior, because she could care less if she gets thrown in a time out. Many kids are WAY too spirited for time outs to work. It's almost better to ignore (which I don't condone) because at least they don't know you "tried" to be the boss.
The behaviors you list are ONLY normal in this age group if you are not disciplining adequately and consistently enough to teach against them. No one likes to be tough, but if you are effective, your life suddenly becomes so much easier, and your kids are so much HAPPIER and full of self pride at acting well, it is WELL worth it. I can honestly say I've never been ANGRY at my kids, because if they're out of control, it's my fault not theirs, and I can take steps to fix it. You don't need to be angry to be an effective disciplinarian, conversely, the most effective disciplinarians I know are sweet, quiet people who speak respectfully to their well behaved kids and do not yell except very rarely.
And don't be so sure that no other kids act like this! My third, for example, was EXTREMELY difficult (still is a huge handful). She was an angry, raging, screaming baby who was deliberate with her aggressive behavior starting at around 9 months. She hit, she kicked, she screamed, she threw fits. She was NOT ALLOWED to proceed. Fits for brushing teath? Consequence. Fits for any reason short of injury, hunger fatigue or genuine sadness? consequence. We NEVER IGNORED a SINGLE FIT (except a couple in settings where we could do nothing). Otherwise, kids run the show by throwing fits. That is not effective parenting, and it's only natural it drives people to yelling.
We (I, husband was hardly home) were most diligent with her between ages of 12 months and 15 months (because she started so early). Now at 2 1/2, she's still super fiery and difficult, and WAY expressive, but does not throw fits or act aggressively. It's not an option, she behaves, especially when we're out and about on errands etc. She's one of those 2 year olds people think are so naturally cute and sweet (eye roll) but it did NOT come naturally, and she was not "born that way". It took WORK and lots of discipline. Many of my family members, each with many kids, have each had at LEAST one very difficult child, if not several. Yes, they take more discipline, but they CAN learn. Also, plenty of difficult kids are out there acting like terrors, so you shouldn't feel like your daughter is somehow worse.
You CAN improve this, but she's pretty set in her ways at 2 1/2, so don't delay if you choose that route! I recommend the book Back To Basics Discipline by Janet Campbell Matson for a timeless and simple approach that WORKS if you use it. Scan it on Amazon to see if it's in alignment with your beliefs. You can be positive and loving most of the time if you are firm enough when you need to be.