Hi, I'm from Shanghai and it's my first time using italki. Please forgive me if I have any mistakes:)

1. Meiyun is helping her mother with the cooking
美云在帮妈妈做饭 perfect

2. Mr. Lee’s friend is from New York
李先生的朋友从纽约来。 perfect, or you can say:李先生的朋友来自纽约。

3. Jack, long time no see.
杰克， 好久不见。 perfect

4. Her sister is rather thin but has a chubby face.
他姐姐瘦瘦的不过有一张圆圆的脸。 perfect

5. Her sister just finished her high school
他的妹妹刚完中学。 他的妹妹刚读完高中。

6. Maming wants his sister to learn computer.
马明想他的妹妹学电脑。马明想让他地妹妹学电脑。

7. Mr. Lin listened to the weather forecast as he drove along.
林先生一边听天气预报一边开车了。 林先生一边开车一边听天气预报。Just don't use "了" here

8. She began to read newspapers as soon as she finished watching the football game.
她一读报纸就完了看足球赛。 她一看完足球赛就开始读报纸。

9. How are you doing? I haven’t heard from you for ages.
你好， 好久没听到你的消息了。 Good, would be better: 你好吗？好久没听到你的消息了。

10. I was almost late yesterday.
昨天我几晚了。 昨晚我差点迟到了。

11. I will buy you a present when I visit Hong Kong.
当我去香港， 我买你一个礼物。 当我去香港的时候，我会给你买一个礼物。

12. Meiyun envies her grandfather because he lives in the countryside.
美云羡慕她的爷爷， 因为他住在郊外（乡村）。perfect