You should know, I'm a weirdo. So, take what I have to say with that in mind:-)
I don't see him doing much of anything wrong. He's a kid and wants to be able to act like a kid. He's not interested in sitting and learning in the boring way that public schools (preschools tend to follow the same type of learning) and so he's rebelling against that. I think it makes total sense.
At 4.5 years old, I think the nap time or quiet time is ridiculous. My son is the same age, and he doesn't need quiet time at all. I know he wouldn't sit quiet for it. He would probably try, but if it's more than 15-20 minutes, that's way too much time. Odds are I'd only get 10 minutes out of him. And, it's not because he's a bad kid, it's because he IS a kid and has a ton of energy and an imagination that he must attend to. He is very bright and is on the go a lot. He would NOT be happy with quiet time that lasted long at all.
Though, I do agree that it's wrong that he is trying to run out into the street and try to overthrow the "government" of preschool (haha!), but at the same time, it makes sense. Kids are meant to learn through play.
So...that's why I'm weird. I really don't see his behavior of refusing to have quiet time, not wanting to go back in after recess, and all that as bad. I see it as a kid not afraid to let people know that he is a kid and needs to be allowed to learn as kids do...through play. They learn SO MUCH that way.
I definitely don't agree AT ALL with them not letting him go out anymore. Honestly, if it were me, I would seriously consider taking him out of preschool (if you are able). It doesn't seem like it's something he likes...and if you look at the studies, sure some preschooled kids do better in kindergarten often, but long-term, there isn't much benefit or signs of being more advanced.
I don't do preschool with my son. Actually I guess I do. He's in kindergarten homeschooled. He spends most of his time playing, but he loves to learn. I keep it limited timewise so that he spends most of his time playing. I keep learning fun and exciting for him. But I know he would probably be behaving just as your son if he was so structured at such a young age. That's not to say I'm anti-structure...just that I think they need the freedom of play.
Okay, I'll stop. Sometimes I just feel a little defensive of the little kids who aren't ready for that type of learning! I totally understand where you are coming from as a parent and in NO WAY want it to sound like I'm criticizing that. Just that I don't think it's something he needs to be punished for or to associate so much negative with when it comes to learning.
Learning should be fun and exciting! :-)