Can someone help me with these sentences?

Which of them are grammatically correct?
Thank you very much in advance.

1) They are not able to dance well.
2) They can't dance well
3) Are you able to play the piano?
4) Can you play the piano?
5) Were you able to find the book you lost?
6) Could you find the book you lost (mistake?)
7) The painting was stolen but returned to the museum a year later.
Harry Potter books hold records/set records as fastest selling books of all time.
8) The painting is protected very well now/is very well protected (?)
9) It is protected by a glass case.
10) Analyze the theme of morality as dealt with by Hardy in his novel Tess of the D’Urbervilles explaining the significance of its subtitle.

Sure, I'd be happy to help you with these sentences.

1) They are not able to dance well. - This sentence is grammatically correct. It uses the verb "are" in conjunction with "able to" to express the inability to dance well.

2) They can't dance well. - This sentence is also grammatically correct. It uses the contraction of "can not" to convey the same meaning as the previous sentence.

3) Are you able to play the piano? - This sentence is grammatically correct. It uses the verb "are" in conjunction with "able to" to inquire about someone's ability to play the piano.

4) Can you play the piano? - This sentence is also grammatically correct. It uses the verb "can" to ask about someone's ability to play the piano.

5) Were you able to find the book you lost? - This sentence is grammatically correct. It uses the past tense of the verb "be" (were) in conjunction with "able to" to inquire if someone was successful in finding a lost book.

6) Could you find the book you lost (mistake?) - This sentence is also grammatically correct. It uses the past tense of the verb "can" (could) to inquire about the ability to find a lost book. There is no mistake in this sentence.

7) The painting was stolen but returned to the museum a year later.
Harry Potter books hold records/set records as the fastest-selling books of all time. - Both of these sentences are grammatically correct. The first sentence describes the events of a stolen painting being returned to a museum, and the second sentence states that the Harry Potter books hold or set records as the fastest-selling books of all time.

8) The painting is protected very well now/ is very well protected (?)- Both of these sentences are grammatically correct. They describe the painting's current state of being well protected.

9) It is protected by a glass case. - This sentence is grammatically correct. It explains how the painting is protected, specifically by a glass case.

10) Analyze the theme of morality as dealt with by Hardy in his novel Tess of the D’Urbervilles, explaining the significance of its subtitle. - This sentence is grammatically correct. It is a command to analyze the theme of morality as presented in Thomas Hardy's novel "Tess of the D’Urbervilles" and to explain the significance of the novel's subtitle.