"Je ne vais pas bien" means that your body and soul don't feel good. You can use it to say that you don't feel good mentally. Also you'll use "Je ne vais pas bien" if you have a long-lasting deadly or very dangerous disease.
"Je ne me sens pas bien" is used to express a state of physical discomfort, like you want to throw up or you feel like you're going to pass out.
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Has difficulty understanding even short answers in this language.
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