Question

1. As he was sick, he could not go out.
2. Being sick, he cound not go out.
3. Sick, he could not go out.
(Are they all the same? Is #3 grammatical?)

4. Reading a book, he chew gum.
5. Shaking hands, he said hello.
6. Smiling brightly, he greeted me.
7. Walking in the park, he thought of the girl.
8. Talking on the phone, he read a comic book.

(Are they all grammatical?)

4-1. While he read a book, he chew gum.
5-1. While he shook hands, he said hello.
6-1. While he smile brightly, he greeted me.
7-1. Whild he walked in the park, he thought of the girl.
8-1. While he talked on the phone, he read a comic book.

(Are they all grammatical and the same as each equivalent?)

Answer 1

1 - 3 all mean about the same thing, but 3 is not a normal structure. "Because he was sick, he could not go out" is best.

4 is OK except for "chew" which should be "chews" or "chewed."
5 - 8 are all fine.

4-1 needs to have "chew" corrected.
5-1 is OK.
6-1 needs to have "smiled" not "smile."
7-1 and 8-1 are fine.