My oldest was similar to this. Never slept, didn't play with toys, grumpy often, difficult to entertain at home, loved preschool. I would say a couple things. First, it is indeed good to have a rough schedule in terms of meals and snacks, just so the day has some structure. Some children at this age find that their nighttime sleep is impacted if they take long naps in the daytime, so his lack of naps may be something you just have to accept. You do have to figure out how to work around it in terms of maybe having a rest time in the middle of the day so that even if he doesn't nap, he at least is laying down and clearing his thoughts, if you see what I mean. Gentle music might be helpful here and once you find something he likes you just play it every single time and it becomes part of his routine.
My kid also was one of those who just pulled all the books off the bookshelf. In retrospect, it was because disorder is easier for a small child to achieve than order. He found any ordered activity to be very difficult (eventual ADHD diagnosis) because it involved motor control and making decisions and so on. You also say he doesn't play with toys. Again this could be because he doesn't have an internal script for that and needs some sort of input from you to build that script. In other words he may want to play WITH you rather than near you. For example, with the books, you can "play a game" where you pick up the books and stack them. This way he can practice the motor skill of picking up books (rather than sweeping them off the shelf).
Do you get stimulation yourself? I found with my child who was like this, that I had to be getting some mental activity in order to come up with things to do with him. Bear in mind, you don't have to always do traditional kid activities. I had a change of perspective when I made friends with a woman who listened to her own favorite music with her toddler! In other words, following your own interests can help.
He may also just need a lot more outdoor time, to work off his energy which again could be a cause of the sweeping of books off the shelf etc.
I know it's hard, when you are up with a small child from that early and they do not nap easily, you get pretty tired by the end of the day.