1) At first he lowered his friend on his rope down the mountain (is it correct to use lower) but as his friend was pulling him off the mountain he decided to cut the rope.

2) He decided to cut the rope so as not to fall off the mountain (is "so as not" correct; what is the difference between fall off and fall down the mountain??)
3) He has his homework done by an online homework agency ( is "have s. done" correct?)
4) He uses the internet to send his homowork to an agency..., that does it for him ( can use be followed by the infinitive in this case?)
5) When Martin Luther King expressed his wish (and hope) for a better world, shouldn't I report his dream using "He wished that in the future...+ would" (instead of "wanted that or dreamed that ...."
6)By introducing a ten-pence bag tax the Irish government obtained a reduction of 90% on the use of plastic bag (and NOT obtained 90% of reduction??)
7)A loyal person never leaves (and NOT qUIT???)the people he loves alone
8)He wanted to divide (is "split up" possible?) good and evil (Or the good and evil sides of human personality)
9) In the 50s there were discrimination laws against black people (is "blacks" also correct?)
10)to proceed on the ice is a synonym for to move on the ice?
11) I can use (is UTILIZE possible) plastic bags many times
12)The only way to stop the transformation was (is the gerund correct??)
13) He discovered that the voice was of the invisible man (OR is it better to say: he discovered it was the voice of the invisible man?)
14) By jumping onto a table the cat knocked over a clock (are "bump" or "hurt" synonyms for knock over?)
15) From that moment onwards (or on) he wasn't able to control ...
16) He had to decide whether to cut the rope and live or hold it and die (is the use of whether correct???)
17) He dreamt that his children would live.... (is it possible????)
Thanks

1) At first he lowered his friend on his rope down the mountain (is it correct to use lower) but as his friend was pulling him off the mountain he decided to cut the rope.

Comma after "first," and you need to clarify the "he" and "him" references. Perhaps it would work better if you have a he and a she!

2) He decided to cut the rope so as not to fall off the mountain (is "so as not" correct; what is the difference between fall off and fall down the mountain??)
"so as not" is slang -- better to write this: "He decided to cut the rope to prevent falling off the mountain." To fall off implies falling umpteen feed off the edge of a cliff; falling down implies falling and rolling down a sloping mountainside.

3) He has his homework done by an online homework agency ( is "have s. done" correct?)
I don't know what "have s. done" means. Your original sentence is correct if you put a period at the end of it.

4) He uses the internet to send his homowork to an agency..., that does it for him ( can use be followed by the infinitive in this case?)
Watch the spelling of "homework." I'd write, "He uses the Internet to send his homework to an agency to be completed."

5) When Martin Luther King expressed his wish (and hope) for a better world, shouldn't I report his dream using "He wished that in the future...+ would" (instead of "wanted that or dreamed that ...."
It's common knowledge that MLK "dreamed..." After all, the famous speech is commonly entitled "I Have a Dream." You can use "dream," "wish," "hope," and yes the auxiliary verb "would" to express all his dreams.

6)By introducing a ten-pence bag tax the Irish government obtained a reduction of 90% on the use of plastic bag (and NOT obtained 90% of reduction??)
Put a comma after "tax," and your original sentence is just fine.

7)A loyal person never leaves (and NOT qUIT???)the people he loves alone
Yes, "leaves" is correct; also be sure to put a period at the end of the sentence.

8)He wanted to divide (is "split up" possible?) good and evil (Or the good and evil sides of human personality)
I'd write, "He wanted to divide the good side of the human personality from the evil."

9) In the 50s there were discrimination laws against black people (is "blacks" also correct?)
I'd write, "In the '50s, there were discriminatory laws against black people." To be clear, in the '50s, the term was "colored" and then "blacks" came into vogue later. Now, however, we use the terminology "African-American," but that was not a '50s term.

10)to proceed on the ice is a synonym for to move on the ice?
Yes.

11) I can use (is UTILIZE possible) plastic bags many times
The word "utilize" would be correct, but pompous. The word "use" is just fine!

12)The only way to stop the transformation was (is the gerund correct??)
If you use the gerund, you'll create a parallelism problem. It'd be better to write, "The only way to stop the transformation was to ."
" target="_blank">http://grammar.ccc.commnet.edu/grammar/parallelism.htm


13) He discovered that the voice was of the invisible man (OR is it better to say: he discovered it was the voice of the invisible man?)
Your second phrasing is better.

14) By jumping onto a table the cat knocked over a clock (are "bump" or "hurt" synonyms for knock over?)
b>YThe words "bump" and "knock over" are pretty much synonyms, but not "hurt."

15) From that moment onwards (or on) he wasn't able to control ...
b>Just use "on."

16) He had to decide whether to cut the rope and live or hold it and die (is the use of whether correct???)
b>Yes, your use of "whether" is correct.

17) He dreamt that his children would live.... (is it possible????)
b>It's fine, but "dreamed" is better.

1) Yes, it is correct to use "lowered" in this sentence. Lower is the correct verb to use when bringing something down from a higher position to a lower position.

2) "So as not" is correct in the sentence "He decided to cut the rope so as not to fall off the mountain." It means "in order to prevent" or "to avoid." "Fall off the mountain" means to descend and possibly drop from the side of the mountain, while "fall down the mountain" generally refers to descending along the slope of the mountain.

3) Yes, "have s. done" is correct in the sentence "He has his homework done by an online homework agency." It is a structure called "causative." In this case, it means that someone else (in this case, the online homework agency) does the homework on his behalf.

4) Yes, "use" can be followed by the infinitive in this case. When we use "use" in this sense, it means to employ or utilize something for a specific purpose, which can be followed by the infinitive verb.

5) Yes, you can use "He wished that in the future... + would" to report Martin Luther King's dream. The phrase "He wished that" introduces a past tense verb, and "would" is used to express a future possibility or hope.

6) The sentence "By introducing a ten-pence bag tax, the Irish government obtained a reduction of 90% on the use of plastic bags" is correct. It is more commonly used to say "obtained a reduction of 90% on" rather than saying "obtained 90% of reduction on."

7) Both "leave" and "quit" can be used in this context. In the sentence "A loyal person never leaves (or quits) the people he loves alone," "leave" means to abandon or desert, while "quit" means to give up or abandon.

8) "Divide" is correct in the sentence "He wanted to divide good and evil." "Split up" can also be used and conveys a similar meaning in this context. Both phrases mean to separate or create a distinction between the two sides.

9) In the sentence "In the 50s, there were discrimination laws against black people," "blacks" can be used as a noun to refer to black people. However, "black people" is more commonly used in contemporary language.

10) Yes, "proceed on the ice" can be synonymous with "move on the ice." Both phrases mean to continue or advance while being on the ice.

11) "Utilize" is possible to use in the sentence "I can utilize plastic bags many times." It means to use something effectively or efficiently.

12) Yes, the gerund "killing" is correct in the sentence "The only way to stop the transformation was ." The gerund functions as a noun in this sentence.

13) Both "the voice was of the invisible man" and "it was the voice of the invisible man" are correct. The first option emphasizes the nature of the voice, while the second option emphasizes the identification of the voice.

14) "Bump" and "hurt" are not direct synonyms for "knock over." While "knock over" means to cause something to fall or tip over, "bump" means to come into gentle or accidental contact with something, and "hurt" means to cause physical or emotional pain.

15) Both "onwards" and "on" are correct in the phrase "From that moment onwards (or on)." They both convey the idea of continuing from that specific moment.

16) Yes, the use of "whether" is correct in the sentence "He had to decide whether to cut the rope and live or hold it and die." "Whether" is used to introduce two or more possibilities or choices.

17) Yes, it is possible to use "dreamt" in the sentence "He dreamt that his children would live." "Dreamt" is the past tense form of "dream" and can be used to indicate a dream as a past event.