I urgently need you to check these sentences. I have a few doubts on how to vary past perfect tenses (when turning the summary into the present). I included my doubts using question marks. Thank you.

1) After moving the bed aside he takes three floorboards, secures the old man between the joints, and replaces the boards. He is proud of himself because there is no blood to wash.
2) At 4 a.m., just when he had finished (?) his work, he answers a knock at his front door. The police are called to go to the house because of the loud noise.
3) When he opens it, three policemen enter, saying a neighbour had reported (??) hearing a shriek and they needed to search the premises. After welcoming the police, he tells them the shriek was (?) his own; he had cried out (?) during a dream.
4) He also tells them that the old man who lived in the house was away in the country. Next, he takes the police all over the house, inviting them to search everything thoroughly.
5) After they enter the old man’s chamber, he points out that the old man’s possessions had not been disturbed. In his growing self-confidence, the narrator brings in chairs and invites the policemen to rest.
6) The police appear completely satisfied that nothing criminal had occurred (?) in the house. However, they continue to chat idly, staying much longer than the narrator had expected (?). entences.

1 - OK

2 - is finishing

3 - reported; OK; cried out

4 - who lives ... is away

5 - have not been

6 - has occurred ... expects

There should be NO past perfect forms. Are you clear on what past perfect is used for and what the sequences of tenses are?

sequence of tenses = http://grammar.ccc.commnet.edu/grammar/verbs.htm#sequence

1) After moving the bed aside, he took three floorboards, secured the old man between the joints, and replaced the boards. He was proud of himself because there was no blood to wash.

To vary the past perfect tense into the present tense, you need to change the verb forms accordingly. For example:
- "After moving the bed aside, he takes three floorboards" becomes "After moving the bed aside, he takes three floorboards."
- "He is proud of himself because there is no blood to wash" becomes "He is proud of himself because there is no blood to wash."

2) At 4 a.m., just when he had finished his work, he answers a knock at his front door. The police are called to go to the house because of the loud noise.

To change from past perfect to present tense, you can follow these steps:
- Change "just when he had finished" to "just when he finishes."
- "He answers a knock at his front door" remains the same.
- "The police are called to go to the house" becomes "The police are called to go to the house."

3) When he opens it, three policemen enter, saying a neighbor had reported hearing a shriek and they needed to search the premises. After welcoming the police, he tells them the shriek was his own; he had cried out during a dream.

For this sentence, you can make the following changes:
- "When he opens it, three policemen enter" becomes "When he opens it, three policemen enter."
- "Saying a neighbor had reported hearing a shriek" remains the same.
- "They needed to search the premises" becomes "They need to search the premises."
- "After welcoming the police, he tells them" becomes "After welcoming the police, he tells them."
- "The shriek was his own" remains the same.
- "He had cried out during a dream" becomes "He cried out during a dream."

4) He also tells them that the old man who lived in the house was away in the country. Next, he takes the police all over the house, inviting them to search everything thoroughly.

To convert this into the present tense:
- "He also tells them that the old man who lived in the house was away in the country" becomes "He also tells them that the old man who lives in the house is away in the country."
- "Next, he takes the police all over the house" becomes "Next, he takes the police all over the house."
- "Inviting them to search everything thoroughly" remains the same.

5) After they enter the old man’s chamber, he points out that the old man’s possessions had not been disturbed. In his growing self-confidence, the narrator brings in chairs and invites the policemen to rest.

To transform this into the present tense:
- "After they enter the old man’s chamber, he points out" becomes "After they enter the old man’s chamber, he points out."
- "That the old man’s possessions had not been disturbed" becomes "That the old man’s possessions have not been disturbed."
- "In his growing self-confidence, the narrator brings in chairs" remains the same.
- "And invites the policemen to rest" also remains the same.

6) The police appear completely satisfied that nothing criminal had occurred in the house. However, they continue to chat idly, staying much longer than the narrator had expected.

To change this sentence to the present tense:
- "The police appear completely satisfied that nothing criminal had occurred in the house" becomes "The police appear completely satisfied that nothing criminal has occurred in the house."
- "However, they continue to chat idly" remains the same.
- "Staying much longer than the narrator had expected" becomes "Staying much longer than the narrator expects."