Can you check if these sentences are possible? Thank you for your invaluable help.

1) Remember to pick the children up at (or from?) the airport.
2) She promised she would give us a lift.
She promised to give us a lift.
3) He is going to take the dog out for a walk.
4) The teacher made him write his homework again.
5) He used to smoke ten cigarettes a day.
10) Ten cigarettes used to be smoked by him.
11) She should water the plants.
12) The police ask us about his nationality. We were asked about his nationality.
13) She is embarrassed at the fine clothes her master had given to her.
but: Her master had given her fine clothes. She was given fine clothes by her master.
14) She can't understand why he didn't have the houskeeper give her the clothes.

Get rid of #10 -- passive just doesn't work for that!!

All the rest are fine, except in #13, you should use "by" instead of "at" (fourth word).

To check if these sentences are possible, we can analyze each sentence individually and determine whether they are grammatically correct and convey the intended meaning.

1) Remember to pick the children up at (or from?) the airport.

Both "at" and "from" can be used in this sentence, but the choice depends on the context. If you are referring to the place where the children will be waiting, you can use "at," as in "Remember to pick the children up at the airport." If you are referring to the point of origin for picking the children up, you can use "from," as in "Remember to pick the children up from the airport."

2) She promised she would give us a lift.
She promised to give us a lift.

Both of these sentences are grammatically correct and have the same meaning. The second sentence is a shorter and more concise version of the first sentence.

3) He is going to take the dog out for a walk.

This sentence is grammatically correct and conveys the meaning that he will be taking the dog out to walk.

4) The teacher made him write his homework again.

This sentence is grammatically correct and means that the teacher forced or instructed him to write his homework again.

5) He used to smoke ten cigarettes a day.
10) Ten cigarettes used to be smoked by him.

Both of these sentences are grammatically correct, but they have slightly different meanings. The first sentence indicates that he personally used to smoke ten cigarettes a day. The second sentence, in the passive voice, suggests that ten cigarettes were smoked by him in the past.

11) She should water the plants.

This sentence is grammatically correct and implies that it would be a good or recommended action for her to water the plants.

12) The police ask us about his nationality.
We were asked about his nationality.

Both of these sentences are grammatically correct, but they have different perspectives. The first sentence is in the present tense and states that the police currently ask us about his nationality. The second sentence is in the past tense and implies that we were asked about his nationality at some point in the past.

13) She is embarrassed at the fine clothes her master had given to her.
Her master had given her fine clothes. She was given fine clothes by her master.

Both of these sentences are grammatically correct and convey the same meaning with slightly different structures. The first sentence suggests that she is currently embarrassed by the fine clothes given to her by her master. The second sentence, in the passive voice, highlights that her master gave her fine clothes.

14) She can't understand why he didn't have the housekeeper give her the clothes.

This sentence is grammatically correct and indicates that she is unable to comprehend the reason why he didn't ask the housekeeper to give her the clothes.

Overall, all the sentences provided are possible and grammatically correct.