1. He stood there, and he closed his eyes.

1-2. He stood there, closing his eyes.
2. He stood there, and then he closed his eyes.
3. He stood there, and after that he closed his eyes.
4. He stood there, with his eyes closed.
5. He stood there with his eyes closed.
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Q1: Do #1 and #1-2 mean #2 or #3? Or do #1 and #1-2 mean #4? Did two actions happen at the same time? Or did one action happened first and the other action followed it after the first action ended?
Q2: Are both Sentence 4 and Sentence 5 okay?

They are all very close. If I had to separate them, I'd put them in two groups ~

In this group, the two actions (standing and closing) are simultaneous: 1-2, 4, and 5.

In this group, the two actions are separate, but happen very close together in time: 1, 2, and 3.

Q1: In #1 and #1-2, the phrase "and he closed his eyes" indicates that two actions happened at the same time. So, #1 and #1-2 mean the same thing - that he stood there and closed his eyes simultaneously.

On the other hand, in #2 and #3, the phrases "and then" and "after that" indicate that one action happened first, followed by the other action. So, #2 and #3 mean that he stood there and then closed his eyes or he stood there, and after that, he closed his eyes.

Q2: Both Sentence 4 and Sentence 5 are grammatically correct and convey a similar meaning. Both sentences indicate that he stood there with his eyes closed. The difference lies in the use of the word "with" in Sentence 4, indicating the state or condition in which he stood there, whereas Sentence 5 simply states the state of him standing there with his eyes closed.