1) He was asked to sort out the mystery about the theft of a ring from Peter's room (is it correct to use theft?)

He had to find the thief of a ring from... (is it correct to use thief?)
2) If I want to help with the plastic bag problem, I have to (or is it better should or will) use plastic bags at least five or six times before throwing them away or use biodegradable ones that disappear in the ground after (or in???) 18 months
3) The use of plastic bags is not banned in many states.(is banned correct?)
4)When the guilty person put the thumb on the saucepan the cockerel would crow. (have the tenses been used correctly?)
5)As his involuntary transformations (into Mr Hyde) became more frequent and having killed an old man (is it correct to use the gerund meaning the reason) he decided to
6) The Black Power Movement was composed of (made up of.. are there any other synonyms??)black people who were dissatisfied with the results of the Civil Rights Movement. It allowed (is it correct?) the use of violence. It was a more militant group (if compared to the C.R.M)Is it correct to use "MILITANT"
7) A sensitive person is someone who gets easily offended (Can you say who is easily offended???)
8) He wanted to live in a world ( or He wished to live/he could live..) where people wouldn't be judged...
9)Could you say he wanted a world where his children....?

Thanks

1. yes = it is a noun

2. I have to use is fine
3. yes
4. yes
#5 = yes
#6 = yes
7. either
8. OK
9. OK

Sra