Hey Lena…well, I really hadn’t considered the passage as a whole to make it more conversational. It would be understandable with those revisions, but you’re correct about “sitting and playing”. If I were to completely rewrite this, I’d probably do it as follows:
A boy came home from school, and his mother asked him, “What a bruise you’ve got under your eye! What happened?”
“I fought with Peter today”
“How did it happen?”
“Well, I was sitting at my desk playing a game on my cellphone, and Pete came up to me and asked to play. I refused, and said that I wanted to play by myself. When he tried to pull the phone out of my hands, I hid it in my bag. That’s when he hit me in the face!”
It’s funny…I know what is correct, and what sounds right, but if you asked me to specifically say what the perfect tense of a particular verb is, I’d have to look it up online to tell you what is right by definition.