Can you check if the following sentences which I turned into the passive voice using the personal construction are correct? Thank you for helping me!

1) They report that Peter is sending her messages.
Peter is reported to be sending her messages.
2) Peter sent her messages/her messages/has sent her messages/had sent her messages.
Peter is reported to have sent her messages.
3) They report that Peter was sending
her messages.
Peter is reported to have been sent her messages.
4) They report they are going to send her messages/will send her messages.
He is reported to be going (???) to send her messages. (can you use it in the future??)
5) He had to decide whether to cut the rope and live or hold the rope and die (is "hold on" possible?)

1) The sentence "Peter is reported to be sending her messages" is correct. You successfully turned the active voice sentence into the passive voice using the personal construction.

2) The sentence "Peter is reported to have sent her messages" is also correct. You correctly used the present perfect tense in the passive voice.

3) However, the sentence "Peter is reported to have been sent her messages" is not correct. It should be "Peter is reported to have been sending her messages."

4) The sentence "He is reported to be going to send her messages" is correct. You can use the future tense in the passive voice.

5) The sentence "He had to decide whether to cut the rope and live or hold the rope and die" is correct. You can also use "hold on" instead of "hold the rope." Both forms are grammatically correct and used interchangeably.

1) Your transformation of the sentence into the passive voice using the personal construction is correct: "Peter is reported to be sending her messages."

To transform a sentence from active to passive voice using the personal construction, follow these steps:
- Identify the subject and the verb in the active voice sentence.
- Change the subject to the person or thing affected by the action (the object of the active voice sentence).
- Use the corresponding form of the verb "to be" followed by the past participle of the main verb. Make sure the tense matches the original active voice sentence.

2) Your transformation of the sentence is mostly correct: "Peter is reported to have sent her messages." However, you may need to clarify the pronoun "her messages." You could consider changing it to "Peter is reported to have sent messages to her."

3) Your transformation of the sentence is incorrect: "Peter is reported to have been sent her messages." In this case, the sentence requires the past continuous tense, not the present perfect. The correct transformation would be: "Peter is reported to have been sending her messages."

4) For the sentence "They report they are going to send her messages/will send her messages," it is not possible to directly form a passive voice sentence using the personal construction. The personal construction is primarily used for reporting what others say or believe about a person's actions. Since the original sentence does not mention who is actually sending the messages, we cannot transform it into passive voice using the personal construction.

5) The sentence "He had to decide whether to cut the rope and live or hold the rope and die" is already in the active voice. However, if you want to transform it into the passive voice using the personal construction, it would be: "It had to be decided whether to cut the rope and live or hold the rope and die." In this case, the focus is shifted from the subject "He" to the action itself. The subject becomes "It," and the verb "had to decide" is changed to the corresponding form of "to be" followed by the past participle of the main verb.