The dog park is one of Levi's favorite places in the world! We've been to several, and I am most comfortable in parks with a separate small dog area because Levi is usually the smallest dog there. Levi is definitely a wrestler, but we've never had any problems as he is very obviously playing - wrestling, running, having a good time.
I always take bags, a collapsible water bowl, and a bottle of water. The park we usually go to does provide bags and water; I just prefer to bring our own. The rules around here are that small training treats are allowed, but long-lasting treats/chews (like bully sticks) are not allowed (to prevent possessiveness and fighting). I've never had to pick Levi up at the park, but I think I would only pick him up in an extreme case.
Have fun! Charlie will love running around and playing with other dogs!