1)Every person that uses a plastic bag (better everyone who uses a plastic bag, has to pay ten pence; is "every time you use a plastic bag, you have to pay...??? correct)

Question

2) one of his servants (also one among his servants?)
3) he said that when the guilty servant put his thumb on the saucepan, the cockerel would crow (are tenses correct?) is when he called out their names, they had to put their thumb ... correct?
4) The Black Powere Movement originated (are there other synonyms?) because some members of the Civil Rights Movement were disappointed with its results (can you say originated out of the dissatisfaction of some members ...??)
5) He wanted that his children have (he wanted his children to have or He wished his children would have the same rights as...)
6) I used the Internet for watching films, chatting with friends and for carrying out school research (is for correct?)
7) The ... movement was created to fight for the civil rights of black people (or black Americans); ... to fight against the discriminatio against black Americans (to fight against racial discriminatio)
8) Pollution is a problem for all countries of or in the world
9) Bags are everywhere even (or also ) in the desert
10) Man is made up of good and evil (or a good and an evil part)
11) A hardworking person improves all the times (how would you correct it?)
12) Move on the ice (better across the ice)
13) Solids is the same as solid objects?
14) He writes on the homepage of the website his questions and he gets his answers (is it correct to use on)
15) Alternatives include the use of human tissue
16) He wanted that blacks won't be judged (wouldn't be judged ..)
17) He uses the Internet for doing his reaserches but he copies what he finds word for word (Can you correct this one?)
Thanks

Answer 1

1)Every person that uses a plastic bag (better everyone who uses a plastic bag, has to pay ten pence; is "every time you use a plastic bag, you have to pay...??? correct)
Your phrasing (both of them!) in parentheses are correct.

2) one of his servants (also one among his servants?)
The first is correct; the second is wordy.

3) he said that when the guilty servant put his thumb on the saucepan, the cockerel would crow (are tenses correct?) Yes.

is when he called out their names, they had to put their thumb ... correct?
Yes.

4) The Black Powere Movement originated (are there other synonyms?)
You can search for synonyms at " target="_blank">http://www.thesaurus.com
because some members of the Civil Rights Movement were disappointed with its results (can you say originated out of the dissatisfaction of some members ...??)
Either phrasing is correct.

5) He wanted that his children have (he wanted his children to have or He wished his children would have the same rights as...)
He wanted his children to have...

6) I used the Internet for watching films, chatting with friends and for carrying out school research (is for correct?)
Delete the second instance of "for" and everything will be fine.

7) The ... movement was created to fight for the civil rights of black people (or black Americans); ... to fight against the discriminatio against black Americans (to fight against racial discriminatio)
Your wording with "Black Americans" is better; "to fight against racial discrimination" (watch the spelling) is best.

8) Pollution is a problem for all countries of or in the world
Either word is correct.

9) Bags are everywhere even (or also ) in the desert
Your original wording is correct.

10) Man is made up of good and evil (or a good and an evil part)
Your original wording is better.

11) A hardworking person improves all the times (how would you correct it?)
A hard-working person tries to improve all the time.

12) Move on the ice (better across the ice)
Both are correct, depending on the rest of the sentence. What is the complete sentence?

13) Solids is the same as solid objects?
Yes.

14) He writes on the homepage of the website his questions and he gets his answers (is it correct to use on)
Better: He writes his questions on his website's homepage, and he gets his answers... (This, too, is incomplete.)

15) Alternatives include the use of human tissue
What's your question here?

16) He wanted that blacks won't be judged (wouldn't be judged ..)
He wanted Blacks not to be judged ...

17) He uses the Internet for doing his reaserches but he copies what he finds word for word (Can you correct this one?)
He uses the Internet to do research, but he copies what he finds word for word.