I forgot to add the following sentences. Thank you very much.

1) When we approached his mother, she went away and set on a bench on her own.
2) Her husband suffers from depression (??) and she doesn't want to talk to anyone, not even with her son.
3) Can you help me put the books back in (?) the bookcase?
4) I fear the weather in Wales will be foggy and rainy just like in England/as in England
5) I think it will be as foggy and rainy as in England.
6) I'm going to get ready for the new school year.
My sister is going to spend only on week on holiday.

1. ... by herself.

2. comma needed

3. OK

4. OK

5. Incomplete comparison.

6. ...only one week ...

1) When we approached his mother, she went away and sat on a bench on her own.

To correct sentence 1, replace "set" with "sat" as it is the correct past tense form of the verb "sit."

2) Her husband suffers from depression and she doesn't want to talk to anyone, not even with her son.
Sentence 2 appears to be incomplete. To make it clearer, you can add the word "even" after "anyone," like this: "Her husband suffers from depression, and she doesn't want to talk to anyone, not even her son."

3) Can you help me put the books back in the bookcase?
Sentence 3 is correct as it is. However, if you are unsure about the location of the books, you can replace the word "in" with "into" to indicate the action of putting the books back inside the bookcase.

4) I fear the weather in Wales will be foggy and rainy, just like in England.
Sentence 4 is correct. It expresses a concern that the weather in Wales will be similar to that in England.

5) I think it will be as foggy and rainy as in England.
Sentence 5 is grammatically correct, but it is redundant. Instead of saying "as foggy and rainy as in England," you can simply say "as foggy and rainy as England."

6) I'm going to get ready for the new school year. My sister is going to spend only one week on holiday.
To combine both sentences, you can say "I'm going to get ready for the new school year, while my sister is going to spend only one week on holiday."