1. He is playing a game with his smart phone.

2. He is talking on the smart phone.

3. He is writing something on his smart phone.

4. Tom and Bill are talking with each other in the corner of the classroom.

5. He is drawing a cartoon.

6. He is reading a comic book.

7. He is running in the classroom to catch his friend.

8. He is laughing with his friends reading a comic book.

9. He is cleaning the floor with a mop.

10. He is mopping the floor.

11. He is sleeping on his desk.

12. He is quarreling with his partner.

(Would you check the sentences? Will you correct some errors, please? thank you.)

I'm thinking #4. It should to talking to eachother not with eachother.

#4 is fine.

There's a problem in #8, though. Who is reading? 'He' or 'friends'?

The sentences you provided are generally grammatically correct. However, there are a few minor errors that can be corrected:

1. He is playing a game on his smartphone. (add "on" before "his smartphone")
2. He is talking on the smartphone. (remove "the" before "smartphone")
5. He is drawing a cartoon. (no correction needed)
6. He is reading a comic book. (no correction needed)
7. He is running in the classroom to catch his friend. (no correction needed)
9. He is cleaning the floor with a mop. (no correction needed)
11. He is sleeping at his desk. (replace "on" with "at")
12. He is quarreling with his partner. (no correction needed)

Overall, the sentences are now error-free.