1. I hope he is running on the playground now.

2. I hope he is studying now.
3. I hope he is playing table tennis now.
4. Is he studying? I hope so.
5. Is he studying (now)? I hope he is studying (now)

6. Is he coming (soon)? I hope so.
7. Is he coming (soon)? I hope he is coming (soon).
8. Will he come soon? I hope he will come soon.
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Are they all grammatical? Is #4 the same as #5?

Do #6, 7, and 8 have the same meaning?
If we think 'soon' is omitted, does #6 mean the near future? Does "I hope he is coming (soon)." mean "I hope he will come (soon)"?

I think you're right about 1-5.

In 6-8, "soon" is needed if you mean that. If you omit that word, it could mean he's on his way whether he arrives "soon" or not.

Yes, all of the sentences you provided are grammatical and make sense.

Regarding #4 and #5, they have similar meanings but there is a slight difference in emphasis. In #4, the speaker is expressing hope for the person to be studying, without mentioning the specific timing. In #5, the speaker explicitly mentions "now" to emphasize the hope that the person is studying at this very moment.

As for #6, #7, and #8, they do have similar meanings but there are subtle differences:

- #6: "Is he coming (soon)? I hope so." Here, the speaker expresses hope that the person will come in the near future without explicitly mentioning "soon." It implies that the speaker hopes for the person's imminent arrival.

- #7: "Is he coming (soon)? I hope he is coming (soon)." In this sentence, the speaker is explicitly stating their hope for the person to come soon. It emphasizes the desire for a prompt arrival.

- #8: "Will he come soon? I hope he will come soon." This sentence expresses hope for the person's prompt arrival, specifically in response to the question of whether or not they will come soon. It directly addresses the timing of the person's arrival and expresses hope for it to happen.

In summary, #6 expresses hope for the person's arrival without explicitly mentioning "soon," while #7 and #8 explicitly address the timing of the person's arrival and express hope for a rapid or prompt arrival.