Much of what she has done is not all that unusual for her age. Many 9 year olds won't fess up, even when you know full well that they did something. If you know for a fact that she did something, don't bother to ask her if she did, that only sets her up to want to lie about it in an attempt to avoid getting into trouble. If it is important enough to merit consequences, then deal with it matter of factly. Many will procrastinate with school work... set a time when it gets started, supervise the work, and let her know she does nothing else until it gets done. Many will shove stuff under the bed, in closets, in drawers, etc. to get it done so they can go play... thinking that you will somehow not notice. Give some incentives if you think it might help... be very specific... clean your room may not be enough, stating that you want her clean clothes put away neatly, dirty clothes in the hamper, and toys on the shelves may give you better results. Put the list on her door if it helps and have her check them off as each one is done. When finished, you can go out for a treat or do something fun.
Certainly talk to her and let her know you are there for her, but she also needs to understand that there will be consequences for her choices. Try not to catch her every time she makes a mistake... pick your battles as to what is really important. Praise the good choices that she makes.
Sit down with her and her father and the three of you discuss how you can all work together to make some changes... discuss expectations... and the importance of learning responsibility. As she sees that you take the time to work with her and guide her, she will understand that you are there for her and that you care about her and what she does.