It’s preschool. Now the book thing I would really question what happened- did someone actually see him viscously hit the girl with the book? did they just see the end of it? Could they have been both pulling at it and he let go and it hit her?
He took his shoes and socks off and ran around? Why did it not get stopped when he was taking his shoes off? What’s the ratio of adults to children?
You don’t have to answer these, just think about it, especially if it seems out of character.
I don’t think those two incidents are that big of a deal alone at that age- now if he was regularly hitting or throwing things, yes.

Maybe he misses his grandma? My child went through the same thing girl. My 8 year old, was 6 then pushed a girl off a chair. And he has adhd.
It will get better, that I can promise you!!