She is two and the job of the two year old is to establish a separate 'me' identity from her parents, test boundaries and learn about the world. She is doing her job. Our job is to make her job safe and fun. That means establishing firm boundaries for dangerous things and making them easy for her. I see nothing in your post to indicate your child is anything but normal.
So if she is a runner (some kids are, they grow out of it) you need to hold her hand when she is near the street. You can make walking together fun (jump, hop, spin in circles, make it a game) but you will have to hold her hand (no amount of spanking will make you 100% sure she won't run into the road, will it?).
She hears 'no' a lot. Toddlers respond better to 'yes' - a positive suggestion or a distraction. It's way easier to 'think of a pink elephant' than to 'not think of a blue rhino'. So when she is playing with the door, you say - we don't play with the door, we play with blocks/trains/whatever you want her to play with, let's do that now. And you lead her away from the door to whatever you will play with together.
For listening - you need to make sure you have her attention. Toddlers (like adults) get engrossed in what they are doing. When I tell DH, 'please remember to pick up milk on the way home' I know that if he does not look at me and say ' ok, do we need chugs too?' that he did not hear me. When I talk to DS, I get down to his level and make eye contact. If he is busy (all the time), I touch him to make sure he is listening. And then I ask him whether he heard me (when he was two, I would have him repeat it).
For things that you have told her not to do, I would consider what they are, how important they are and why she is doing them. For example - 'do not play with those books'. For me not ruining books is important so I would set a boundary. Next - where are the books? If they are too accessible, I would move them - avoiding temptation. Why is she playing with them? Well, they are bright and colorful and she can manipulate them (all good reasons). So I would give her something else she can play with that is similar. Finally - can she interact with them in a 'safe way'? Yes, I can take them out, let her use one finger touch and look at them together.
I try to look at interaction with DS as having a win win potential NOT as a zero sum game (where I need to 'win' every interaction). I do NOT need to be right every time. It's ok if I change my mind if DS is right. It's ok if I take a moment to think about whether the statement that just came out of my mouth is good or is just something that was a reflex (stay away from the steps, we don't climb steps!, hmmm, why not, maybe it's time to learn to climb steps).
After all, I am not just raising a child. I am raising a person who I hope will become a thinking, reasoning, empathetic adult who is able to compromise and negotiate. I want my child to learn these things from DH and myself, so I need to model them.
I am not a fan of highly structured programs for youngsters but there are kids who thrive in them.