Can you please check if everything is correct? Thank you very much.

1) Hamlet wonders whether he should make a stand against his sea of troubles or leave things as they are. 2) He believes that both active and passive resistance is bound to meet failure.
3) Death will be the result of any action he may take either by committing suicide or as a retribution for killing Claudius.
4) He wonders whether he should offer passive or active resistance.
5) Hamlet seems to turn more specifically to suicide.
6) The idea of death is divided into sleep, which is desirable and dreams.
He wonders whether there will be dreams after death.
7)After doing the shopping you go to the cash desk (or check-out counter), put your items on the conveyor belt and pay for them by credit card or cash.
8) In Italy you buy the newspaper at the newsagent's and the cigarettes at the tabacconist's. You can find a tabacconist's half way through the main street. There's a leather goods shop on the corner between Oxford Street and Tate Street opposite the baker's.

1) Hamlet wonders whether he should make a stand against his sea of troubles or leave things as they are. OK

2) He believes that both active and passive resistance is bound to meet failure. This reads awkwardly because "both" indicates a plural, but the subject and verb are singular. Please rephrase.

3) Death will be the result of any action he may take either by committing suicide or as a retribution for killing Claudius. OK

4) He wonders whether he should offer passive or active resistance. OK

5) Hamlet seems to turn more specifically to suicide. OK

6) The idea of death is divided into sleep, which is desirable and dreams.
He wonders whether there will be dreams after death. Rethink the punctuation in the first sentence.

7)After doing the shopping you go to the check-out counter, put your items on the conveyor belt, and pay for them by credit card or cash. Notice word change and punctuation, too.

8) In Italy you buy the newspaper at the newsagent's and the<~~delete "the" cigarettes at the tabacconist's. You can find a tabacconist's half way up main street. There's a leather goods shop on the corner between Oxford Street and Tate Street opposite the baker's.

I can help check the correctness of the statements you provided. Let's go through them one by one:

1) Hamlet wonders whether he should make a stand against his sea of troubles or leave things as they are.
- This statement is grammatically correct. It describes Hamlet contemplating whether to take action or maintain the status quo.

2) He believes that both active and passive resistance is bound to meet failure.
- This statement is grammatically correct. It conveys Hamlet's belief that regardless of the type of resistance (active or passive), it will ultimately fail.

3) Death will be the result of any action he may take either by committing suicide or as a retribution for killing Claudius.
- This statement is grammatically correct. It explains that Hamlet anticipates death as a consequence of any action he chooses: either by taking his own life or as a result of seeking revenge for Claudius' actions.

4) He wonders whether he should offer passive or active resistance.
- This statement is grammatically correct. It reflects Hamlet's contemplation about the two types of resistance - passive or active - and the decision he needs to make.

5) Hamlet seems to turn more specifically to suicide.
- This statement is grammatically correct. It suggests that Hamlet's focus shifts towards considering suicide as a possible option.

6) The idea of death is divided into sleep, which is desirable, and dreams. He wonders whether there will be dreams after death.
- This statement is grammatically correct. It describes Hamlet's reflection on the concept of death, particularly the division between sleep (which he finds desirable) and dreams. He also questions whether there will be dreams after death.

7) After doing the shopping, you go to the cash desk (or check-out counter), put your items on the conveyor belt, and pay for them by credit card or cash.
- This statement is grammatically correct. It presents a general sequence of actions involved in completing a shopping transaction.

8) In Italy, you buy the newspaper at the newsagent's and the cigarettes at the tabacconist's. You can find a tabacconist's halfway through the main street. There's a leather goods shop on the corner between Oxford Street and Tate Street, opposite the baker's.
- This statement is grammatically correct. It provides information about purchasing a newspaper and cigarettes in Italy, a location of a tabacconist's, and the presence of a leather goods shop in a specific area.

Overall, all the statements are grammatically correct based on the information provided.