1. Who is taking care of the children while your are away?

2. Who will take care of the children while your are away?

(Does #1 mean #2? Or does #1 mean who is in the process of doing somthing "now"?)

3. "Is he coiming?" "I hope so."
4. Will he come? I hope that he will come.
5. Is he coming now? I hope he is coming now.
(Does #3 mean #4 or #5?)

1 and 2 -- You need "you're" (not "your") since you are really saying "you are..."

Both 1 and 2 mean the same thing once you fix that error.

3 means 5; they are about the present. 4 is asking about the future.

Thank you for your help.

1. Who is taking care of the children while you are away?

2. Who will take care of the children while you are away?

(Does #1 mean #2? Or does #1 mean who is in the process of doing somthing "now"?)

3. "Is he coiming?" "I hope so."
4. Will he come? I hope that he will come.
5. Is he coming now? I hope he is coming now.
(Does #3 mean #4 or #5?)
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(What about this one?)

6. Is he coming this evening? I hope so.
I hope he is coming this evening.

7. Will he come this evening? I hope so.
I hope he will come this evening.

(In this case, are #6 and #7 the same?)

1. In the sentence "Who is taking care of the children while you are away?" the use of the present continuous tense "is taking" suggests that someone is currently in the process of taking care of the children while you are away. It implies that there is an ongoing action or responsibility being undertaken by someone at the present moment.

2. In the sentence "Who will take care of the children while you are away?" the use of the future tense "will take care" indicates that someone will be responsible for taking care of the children at some point in the future. It suggests that arrangements or plans are being made for the care of the children during your absence.

So, there is a difference in meaning between the two sentences. Sentence 1 (Who is taking care of the children while your are away?) refers to the current situation and implies that someone is actively and presently taking care of the children. Sentence 2 (Who will take care of the children while your are away?) refers to a future event or arrangement and indicates that someone will be responsible for taking care of the children in your absence.

Regarding your second question:

3. The conversation "Is he coming?" "I hope so." suggests that there is uncertainty about whether the person in question will arrive or not. The speaker expresses a hopeful expectation that the person will come.

4. The sentence "Will he come?" implies that the speaker is asking about someone's future action or plan to come. The speaker expresses hope that the person will indeed come, indicating a desire for the person's presence.

5. The sentence "Is he coming now?" refers to the current moment and suggests that the speaker is inquiring about whether the person is in the process of coming at the present time. The speaker expresses hope that the person is currently coming, indicating a desire for the person's immediate presence.

So, there are slight differences in meaning between these three sentences. Sentence 3 expresses uncertainty about the person's arrival at some unspecified time in the future. Sentence 4 focuses on the future action of the person, while expressing hope for their arrival. Sentence 5 refers to the present moment, seeking confirmation that the person is currently on their way, with hopeful anticipation of their immediate arrival.