Only #1 is possible. The others are not possible because the main subject and the subject of the non-finites are not the same, among other problems. You need to stop experimenting with textbook patterns and start paying attention to English as it is used: 1) I'm a foreigner, so I can't speak English.
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park sang joonWhy is #2 ungrammatical?It is not ungrammatical—it is nonsensical.