The basic purpose of #2 is to add emphasis. In spoken English, we may also say 'She made the cookies' and then decide we should have said 'Sarah made the cookies'. In other words, 'Sarah did' can simply be an afterthought.
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Anonymous1. When do you use (2)? (On what occasions? Written or spoken?)I virtually never use (2), either in writing or speaking. If I said it, it would be just as a joke, a sort of imitation of people who speak like that, of whom there are very few anymore these days, as far as I know.