Well, he's a healthy 2 year old. That's how they are.
Part of your job as a parent is to set and enforce boundaries. You shouldn't expect him to be a perfect little angel, but you can lay down the law with certain things.
Him hitting, pushing, biting, etc. isn't acceptable and you can't tolerate it. Time out, loss of privilege, even spanking. Do whatever you have to do. Make sure he know that those things are not allowed and if he does them, there will be consequences.
Being a slob and breaking things; that's more of a misbehavior that you can work on over time. Praise for picking things up and playing gently with things is best. If he's deliberately destroying things in an attempt to anger you, then you treat that the same as if his aggression were physically directed toward you.
Remember that he desires your attention. If you don't give him the positive attention that he needs for behaviors you like, then he'll learn to get your attention by doing negative things.
The most important thing you said is that you're at the end of your rope.
You need time to get away from chasing a two foot terror, be an adult, and relax. That means you have to enlist others to help you care for him so you can unwind. Grandparents are great for this. Sticking daddy with him for a day so you can go get a mani-pedi is a great little escape for a mommy.