Your passage is mostly correct and easy to understand, but I will explain it step by step to help you see why it works and where we can improve it slightly.

Original passage:
"Every part of the city feels different. The centre is noisy with cars and buses. The old town is pretty and full of visitors. In quiet residential areas, children play outside, while mothers push strollers. The amusement park is alive with joyful shouts."

Step 1: Sentence 1: "Every part of the city feels different." – This sentence is correct. It clearly says that different places in the city feel unlike each other.

Step 2: Sentence 2: "The centre is noisy with cars and buses." – This is also correct. Note: "centre" is the British English spelling. If using American English, "center" is preferred.

Step 3: Sentence 3: "The old town is pretty and full of visitors." – This is good. "Pretty" describes the town well, and "full of visitors" makes sense.

Step 4: Sentence 4: "In quiet residential areas, children play outside, while mothers push strollers." – This sentence is clear, but you could add a small comma before "while" if you want. It's optional.

Step 5: Sentence 5: "The amusement park is alive with joyful shouts." – This sentence is a bit poetic and correct as it is. "Alive with joyful shouts" means there is a lot of happy noise.

Overall, your text is grammatically correct and very good for an 8-year-old. Just remember the spelling difference of "centre" vs. "center" depending on which English you use.