Questions about example sentences with, and the definition and usage of "Inspector"

A: “You need to hire a home inspector before you buy a house."

"The health inspector suggested that the restaurant close for repairs."

“The inspector checked the report”

“The deputy inspector is in charge of our case”

A: in-spek-tuhs

A: custom officer? pero no sé si es lo que quieres decir

A: Tax inspector

A: × The inspector pointed out the daddy of the dead kid as suspect
✓ The inspector pointed out the father of the dead kid as suspect

"Daddy" sounds more like a childish term and on a bizarre note sometimes people use it to call their lovers in a sexual way 😅so it has that weird informal connotation. "father" is more formal and fit here

A: × I explained an inspector about the result of the product test conducted last week.
✓ I explained the result of the product test conducted last week to an inspector.

× I had enough time to make a preparation to explanation.
✓ I had enough time to make a preparation to give an explanation/I had enough time to prepare my explanation.

× So I could get the approval of the result from him.
✓ Hence, I got the result's approval from him.

In the first sentence, inverting the sentence gives it more clarity imo.
Having time to make a preparation is correct, but preparation to 'give an' explanation would be correct, although unnatural. "I had enough time to prepare my explanation" is more accurate and I understand it means the same thing.
You are using past tense throughout the sentence, and in the last sentence you changed it to a conditional verb tense (could), which is hypothetical, which would be unclear. Hence, either you got or did not get the approval of the result. Otherwise, change all sentences to the conditional verb tense (could, would, should).
I hope I helped!

A: An inspector = French, I think.

1. Airport security, the police or federal agents are likely to do this in the U.S.

2. You don't phrase check people like this, you check spaces (places like this). You can say looking everyone over.

3. You find people, but you "find out" information. So "out" doesn't belong here.

An inspector¹ at the airport is checking *people up and down*² to *find out³* terrorists that are reported to have sneaked into the airport.

A: hope it helps🐣

A: The word ''Was'' is used to describe an action that happened in the past. You could say ''The inspector was walking and bumped his leg on the cart.'' If you're talking about something that happened in the present you would say ''The inspector bumped his leg on the cart.''