Sentence 4 is very awkward, but the others are fine. The two actions in each sentence are simultaneous, yes.
I wouldn't use #4.
Thank you very much for your help. Here go some more sentences related to participal construction.
1. He was standing there, and he closed his eyes.
(Did he close his eyes later? Or was two actions done at the same time?)
2. He was standing there, closing his eyes.
3. He was standing there while he closed his eyes.
4. He was standing there, his eyes being closed. (by him)
5. He was standing there, with his eyes closed.
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Are they all the same in meaning? Do we have to add 'by him' in #4?
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