In my original version I had the simple past and past perfect. I tried to use the simple present (in place of the simple past) and nearly always the present perfect (in place of the past perfect). However, I’m still unsure.

Question

Could you please check them again?

1)The following morning he is very polite to the old man and continues to carry out his duty asking the man how he had spent (not “has spent”) the night.
2)At 4 a.m., just when he has finished his work, the narrator answers a knock at his front door. When he opens it, three policemen enter, saying a neighbour had reported hearing a shriek and they needed to search the premises.
3)After welcoming the police, he tells them the shriek was his own; he had cried out (not has cried out) during a dream.
4)He also tells them that the old man who lives in the house is away in the country. Next, he took the police all over the house, inviting them to search everything thoroughly.
5)After they enter the old man’s chamber, the narrator points out that the old man’s possessions has not been disturbed.

Answer 1

"had" is the auxiliary verb to form the past perfect tense.

"has" or "have" are the auxiliary verbs to form the present perfect tense.

Rethink them all.