As for the second sentence I'm pretty sure that the falling is a participle. In fact, the whole phrase' falling for him all over again' functions as an adjective phrase modifying the subject she, I think. Since there is no such clear correlation in the first sentence I can't be sure as to whether the picking is a gerund or participle but the former seems more likely to me.
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WowenglishI wonder if "picking and falling" is "present particle" or anything. What's the big idea, picking on my little sister? What a fool she was, falling for him all over again.The term you want is "present participle". There is certainly a case to be made for that interpretation. The near-equivalent paraphrases are something like t