North The gerund is a present participle which is used as a noun in a sentence. So let's examine your sentence #1. Mrs Smith was the first (person) to receive the prize.
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northwinddon't understand the difference between #1 and #2, and #3 and #4first to receive is the most usual phrasing.
northwindwhat you feelHmmm. I feel puzzled. I think, "Hmmm. Is there any case where the pronouns first (one), last (one), only one, and so on, chiefly superlatives, are followed by a present participle. I can't think of any. But maybe there are some cases where it happens. I don't know which cases those would be. Hmmm. This is puzzling. It d