Questions & Answers about Мальчик заигрался с новой игрушкой.
How do the prefix за- and the postfix -ся change the verb играть (to play) here?
In Russian, adding both за- and -ся to a verb often creates a meaning of absorption or excess. It means the person got so caught up in the action that they lost track of time or crossed a reasonable limit. So, заиграться means to get carried away playing.
Is заигрался perfective or imperfective? Since he played for a while, shouldn't it be imperfective?
Заигрался is perfective. This is a common trap! Even though the playing itself took a long time, the verb focuses on the result of that process: the state of having gotten too absorbed. The shift from normal playing to being completely carried away is a completed, perfective event.
Does заигрался imply something negative?
Not strictly negative, but it usually implies a consequence. It means the boy played longer than he was supposed to, perhaps missing dinner, forgetting his homework, or just ignoring the world around him. It emphasizes crossing a boundary of time or attention.
Could I drop the preposition с and just say заигрался новой игрушкой?
No, you need the preposition с (with) here. While some Russian verbs take a bare instrumental object to show what instrument is being used, verbs of playing generally require с plus the instrumental case when you are talking about the physical object or person you are playing with.