1. Please water the plants while I am away.

2. Please water the plants while I am absent.

3. Please water the plants in my absence.

4.Please water the plants while I am not here.

5. Please water the plants while I am out.

6. Please water the plants while I am on a business trip.

7. Please water the plants while I am at work.

(Are they all grammatical? Are the expressions from #1 to #5 the same? Thank you for your help.)

1, 3, 4, and 6 mean about the same thing.

2, 5, and 7 mean a more temporary absence -- like being absent from class or work or like being out for the evening -- but not away from home on a trip of several days or a week or more.

Yes, all of the expressions provided are grammatically correct. While they convey similar meanings, there are slight differences in nuance:

1. "Please water the plants while I am away" and "Please water the plants while I am not here" both imply that the speaker will not be present, but do not specifically mention the reason for their absence.

2. "Please water the plants while I am absent" and "Please water the plants in my absence" suggest a more formal tone, as "absent" is a more formal term compared to "away" or "not here."

3. "Please water the plants while I am out" implies that the speaker will be away temporarily, but it does not provide specific information about the reason for their absence.

4. "Please water the plants while I am on a business trip" and "Please water the plants while I am at work" both indicate the specific reason for the speaker's absence. "On a business trip" implies that the speaker is away for work-related reasons, while "at work" implies that their absence is due to their job responsibilities.

In summary, while all of the expressions are grammatically correct, they differ slightly in tone and specificity regarding the reason for the speaker's absence.