Yes, under the circumstances Jem's bahavior seems understandable and typical. After all, he is a great deal older than Scout, and he could get tired of having her following him around. Children can be terribly cruel to each other. Scout is probably fortunate that he pays as much attention to her as he does. Evidently he doesn't have many boys his own age to play with; otherwise he would abandon her much more frequently. We feel very sorry for Scout when Jem leaves her to her own devices. It seems like a strange town, in which there aren't many girls for Scout to play with and not many boys for Jem to play with. Normally in that kind of a sibling situation, the older boy would be spending all his time playing with boys his own age, and he would have more mobility than a young girl Scout's age. Normally she would be playing with girls her own age or with younger boys. Scout is very intelligent. She seems to understand why Jem gets impatient with her and why he wants to have freedom and privacy.
YES. Jem is maturing. He is thinking more, experiencing more emotion, and wanting to be like his father more. He wants to branch out from Scout Dill. Basically, during that time, he wants to become his own person.